Investigations of Non-Covalent Carbon Tetrel Bonds by Computational Chemistry … · 2017-01-31 · Investigations of Non-Covalent Carbon Tetrel Bonds by Computational Chemistry and

© Scott A. Southern, Ottawa, Canada, 2016

Investigations of Non-Covalent Carbon Tetrel Bonds by

Computational Chemistry and Solid-State NMR Spectroscopy

Scott Alexander Southern

A thesis submitted to the Faculty of Graduate and Postdoctoral Studies in

partial fulfillment of the requirements for the degree of

Master of Science

Ottawa-Carleton Chemistry Institute

Department of Chemistry and Biomolecular Sciences

Faculty of Science

University of Ottawa

II

Table of Contents

List of Figures ............................................................................................... IV

List of Tables .................................................................................................. X

Abstract ...................................................................................................... XIII

Acknowledgements ..................................................................................... XV

Statement of Originality ............................................................................. XIX

Chapter 1 - Introduction .................................................................................. 1

1.1 The Basic Properties of Matter ................................................................. 1

1.2 Noncovalent interactions ........................................................................... 5

1.2.1 Sigma-Holes .................................................................................................... 8

1.2.2 Sigma Hole Bonding ..................................................................................... 11

1.3 Group IV “Tetrel” Bonding .................................................................... 13

1.4 Nuclear Magnetic Resonance Spectroscopy ........................................... 17

1.4.1 The Zeeman Interaction ................................................................................ 17

1.4.2 Magnetic Shielding ....................................................................................... 22

1.4.3 Spin-spin coupling ........................................................................................ 24

1.4.4 Other NMR interactions ................................................................................ 25

1.5 Objectives ................................................................................................ 26

Chapter 2 - Instrumentation and Methodology ............................................. 28

2.1 Sample Preparation ................................................................................. 28

2.1.1 Introduction to Theoretical Aspects of Powder X-Ray Diffraction .............. 28

2.2 Quantum Computational Chemistry ....................................................... 29

2.2.1 The Hartree-Fock Method and the Self Consistent Field .............................. 29

2.2.2 Møller-Plesset Perturbation Theory .............................................................. 35

2.2.3 Density Functional Theory ............................................................................ 36

2.2.4 Computation of NMR Parameters using DFT............................................... 40

2.2.5 Gauge Including Projector Augmented Wave DFT Calculations ................. 41

2.2.6 Counterpoise Correction ............................................................................... 42

2.3 Experimental Methodology of SSNMR .................................................. 43

2.3.1 Experimental Setup ....................................................................................... 43

2.3.2 Magic Angle Spinning .................................................................................. 45

III

2.3.3 Sensitivity Enhancement ............................................................................... 46

2.3.3.1 Cross-Polarization ............................................................................................. 46

2.3.3.2 Data Acquisition Periods .................................................................................. 48

2.4 Experimental Methods ............................................................................ 49

2.4.1 Sample Preparation ....................................................................................... 49

2.4.2 Powder X-ray Diffraction – Experimental Methods ..................................... 50

2.4.3 Cluster Model Analysis ................................................................................. 50

2.4.4 Solid-State NMR ........................................................................................... 52

2.4.5 GIPAW DFT ................................................................................................. 52

Chapter 3 - Results and Discussion ............................................................... 54

3.1 Computational Investigations of NMR Trends in Tetrel Bonds ............. 54

3.2 Experimental NMR Investigations of Noncovalent Tetrel Bonds .......... 70

Chapter 4 - Conclusions ................................................................................ 83

References ..................................................................................................... 85

Appendix I – Supplementary Data .............................................................. 103

Appendix II – Sample of Computation Input Files ..................................... 121

Gaussian Input for the Geometry Optimization of Acetylene ........................ 121

Gaussian Input for NMR calculation of Magnetic Shielding Contributions .. 122

Gaussian Input for NMR calculation of J-coupling ........................................ 123

IV

List of Figures

Figure 1. A basic representation of a 12C atom using the Rutherford-Bohr model. The nucleus

(blue) is surrounded by the orbit of electrons occupying two energy levels. Two

electrons (yellow) reside in the n=1 shell, and four in the n=2 shell. Note that

further electronic orbitals may exist beyond those that are occupied in the case of

an excited electronic state. .................................................................................... 2

Figure 2. The electronic configuration diagram for a single fluorine atom (1s22s22p5). The

filling of the molecular orbitals, with increasing energy, follows Hund’s rule. ... 4

Figure 3. The hydrogen bond. The electrostatic interactions between the partially positive

(δ+) and partially negative (δ-) charge contribute to an attractive interaction

between the oxygen and hydrogen atoms in water molecules. ............................. 6

Figure 4. The electrostatic potential at the 0.001 a.u. surface of various structures exhibiting

σ-holes. The σ-hole is present on (b) chloromethane; (c) fluoromethane; (d) a

methyl group that is covalently bonded to methylammonium. For illustration

purposes, a molecule of methane (a) is shown and does not to possess a sigma hole

on carbon. Instead, the area where the hole ought to be is more negative due to

the electronic depletion over the hydrogen atoms (each of which coincidently

possess a single hole15). The red colour corresponds to electrostatic potential

values ≤ 0.172 a.u. and the blue colour corresponds to electrostatic potential values

≥ 0.179 a.u. .......................................................................................................... 10

Figure 5. General schematic of a tetrel bond, where R is a covalently bonded atom or

functional group, X is the tetrel bond donor (X = C, Si, Ge, Sn, or Pb), and Y is

V

the tetrel bond acceptor.40 dX-Y is smaller than the sum of the van der Waals radii

of the interacting atoms. ...................................................................................... 12

Figure 6. (a) The electrostatic potential at the 0.001 au surface of positively charged

dimethylammonium (left) and formaldehyde (centre) computed by CAM-

B3LYP/6-311++G(d,p). The red colour on dimethylammonium (right)

corresponds to electrostatic potential values ≤ 0.172 au; the blue colour

corresponds to electrostatic potential values ≥ 0.179 au. The -hole is present on

the methyl carbon and is adjacent to the C-N -bond, and it has an electrostatic

potential value of 0.179 au. (b) A carbon tetrel bond involving a methyl carbon.

(c) An example of a carbon tetrel bond occurring in the crystal structure of

sarcosinium tartrate. ............................................................................................ 14

Figure 7. A schematic showing the influence of a tetrel bond on the activation of an SN2

reaction. Inspired from the work of Grabowski.56 Purple: fluorine; Grey: carbon;

White: hydrogen; and Yellow: chlorine. ............................................................. 15

Figure 8. The Zeeman Effect for a spin-½ nuclide. The splitting of the spin states is observed

as a function of the strength of the magnetic field. ............................................. 20

Figure 9. A 9.4 T NMR spectrometer magnet for the solid state. The superconducting coil is

found within the large cylindrical container, which also houses the cooling liquid.

............................................................................................................................. 44

Figure 10: Typical single pulse cross polarization pulse program. A 𝜋

2 pulse is applied to the

proton channel, followed by a 1H 13C contact time. This is followed by the

acquisition period coinciding with decoupling from the protons. ....................... 48

VI

Figure 11. The increase of the signal-to-noise ratio as a function of the number of time

dependent scans. Initially, the signal intensity grows rapidly, but as time continues

to increase, the interval at which the signal gain is achieved becomes impractically

long. ..................................................................................................................... 49

Figure 12. A 4 mm MAS rotor compared to a Canadian Penny for scale. The cap of the rotor

is winged so that it may spin using a high pressure air stream. The spinning speed

is adjusted using an MAS controller fit onto the spectrometer console. ............. 52

Figure 13. Cost analysis of the various methods used in the test study on model 6. The red

hashed line represents the energy difference cut-off for this study at 0.5 kcal/mol,

as compared to the energy obtained in the QCISD calculation. All energies are at

a tetrel bond distance of 2.825 Å. The time taken for the QCISD calculation was

5,232 s. ................................................................................................................ 56

Figure 14. Model compounds containing carbon tetrel bonds between methyl carbons and

oxygen-containing functional groups. ................................................................. 57

Figure 15. A schematic showing how the tetrel bond lengths of the model compounds are

modified for the computations. The bond lengths are changed in 0.10 Å increments

from 2.825 Å to 3.325 Å. The atomic coordinates are modified in the GaussView

software. .............................................................................................................. 58

Figure 16.. NMR computational investigations of model compounds. Calculated isotropic

chemical shifts of model compounds using (a) MP2, (b) B3LYP, (c) LC-PBE,

(d) LC-PBE-D3, (e) BHandHLYP, and (f) CAM-B3LYP are plotted against the

reduced distance parameter (rC∙∙∙Y) (top axis) and the interaction distance (d

VII

(C∙∙∙Y)) (bottom axis). Each plot is fit by a quadratic polynomial function with R2

> 0.99 for all methods except CAM-B3LYP (Table 12-Table 17). For spacing,

data values for structures 8, 9, 13 and 14 are found in Table 6 to Table 8 in

Appendix I – Supplementary Data. ..................................................................... 60

Figure 17. Computed CP corrected interaction energy values vs. interaction distance of the

model compounds. Computed interaction energies using (a) MP2, (b) B3LYP, (c)

LC-PBE, (d) LC-PBE-D3, (e) BHandHLYP, and (f) CAM-B3LYP are plotted

against the reduced distance parameter (rC∙∙∙Y) (top axis) and the interaction

distance (d(C∙∙∙Y)) (bottom axis). The calculated interaction energies of the model

compounds were obtained by 6-311G++(d,p) with each respective functional.

Each plot is fit by a quadratic polynomial function with R2 > 0.96 (Table 12 to

Table 17 in Appendix I – Supplementary Data). ................................................ 64

Figure 18. Computed J-coupling for model compounds. Graphs represent 1cJ-coupling

values between 13C and either 17O or 15N using (a) The LC-PBE-D3, (b)

BHandHLYP, and (c) CAM-B3LYP methods. In each case, the 6-311++G(d,p)

basis set is used. Each plot is fit by a quadratic polynomial function with R2 > 0.99

(Table 9 to Table 11 in Appendix I – Supplementary Data).............................. 70

Figure 19. The tetrel bond present in N,N,N’,N’-tetramethylethylenediammonium succinate

succinic acid. The interaction distance is 3.07 Å. ............................................... 71

Figure 20. Powder X-Ray diffractogram of sarcosine. The simulated diffractogram (a) was

obtained using the Mercury version 3.5.1 software provided by the CCDC. The

VIII

experimental diffractogram (b) was obtained from a powdered sample using a

Rigaku Ultima IV X-ray diffractometer. ............................................................. 73

Figure 21. Powder X-Ray diffractogram of sarcosinium tartrate. The simulated

diffractogram (a) was obtained using the Mercury version 3.5.1 software provided

by the CCDC. The experimental diffractogram (b) was obtained from a powdered

sample using a Rigaku Ultima IV X-ray diffractometer. .................................... 74

Figure 22. Powder X-Ray diffractogram of N,N,N’,N’-tetramethylethylenediammonium

dichloride. The simulated diffractogram (a) was obtained using the Mercury

version 3.5.1 software provided by the CCDC. The experimental diffractogram (b)

was obtained from a powdered sample using a Rigaku Ultima IV X-ray

diffractometer. ..................................................................................................... 75


succinate succinic acid. The simulated diffractogram (a) was obtained using the

Mercury version 3.5.1 software provided by the CCDC. The experimental

diffractogram (b) was obtained from a powdered sample using a Rigaku Ultima

IV X-ray diffractometer. ..................................................................................... 76

Figure 24. 13C CP/MAS spectra of sarcosine (top) and sarcosinium tartrate (bottom).

Spinning sidebands are denoted with asterisks. 𝐵0 = 9.4 T. ............................... 77

Figure 25. Selected regions of experimental 13C cross-polarization magic-angle spinning

(CP/MAS) NMR spectra of the methyl carbon associated with a tetrel bond. 𝐵0 =

9.4 T. (a) Sarcosinium Tartrate. (b) Sarcosine. ................................................... 78

IX

Figure 26. 13C CP/MAS spectra of N,N,N’,N’-tetramethylethylenediammonium dichloride

(top) and N,N,N’,N’-tetramethylethylenediammonium succinate succinic acid

(bottom). Spinning sidebands are denoted with asterisks. 𝐵0 = 9.4 T. ............... 79


(CP/MAS) NMR spectra of the methyl carbon associated with a tetrel bond. 𝐵0 =

9.4 T. (a) N,N,N’,N’-tetramethylethylenediammonium dichloride. (b) N,N,N’,N’-

tetramethylethylenediammonium succinate succinic acid. ................................. 80

X

List of Tables

Table 1. Typical interaction strength of noncovalent interactions compared to some

examples of covalent bonds. A variety of examples were selected to present an

idea of expected interaction energy strengths. ...................................................... 7

Table 2. Functionals compared to QCISD in order to set a benchmark for determining the

highest performing functional as it applies to carbon tetrel bonding. ................. 55

Table 3. Computed values of the diamagnetic and paramagnetic contributions to the

magnetic shielding constants (d, p, and t) for the model structures. Values were

calculated by B3LYP and LC-PBE using the 6-311++G(d,p) basis set. .......... 65

Table 4. Computed chemical shift anisotropy data for model compounds using stated

functionals using the 6-311++g(d,p) basis set. .................................................... 67

Table 5. Calculated GIPAW and experimental 13C isotropic chemical shifts for the methyl

carbon on sarcosine compounds. ......................................................................... 81

Table 6. Raw data obtained from calculations (BHandHLYP/6-311++G(d,p)) of

1cJ(13C,17O/15N) in model structures. All values are reported in Hz. ................ 103

Table 7. Raw data obtained from calculations (LC-PBE-D3/6-311++G(d,p)) of


Table 8. Raw data obtained from calculations (CAM-B3LYP/6-311++G(d,p)) of


Table 9. Polynomial fit information for 1cJ(13C,17O/15N) vs the carbon tetrel bond length

(BHandHLYP/6-311++G(d,p)). ........................................................................ 111

https://d.docs.live.net/f14659b146ca583e/Thesis/Corrections/Master%20(Repaired).docx#_Toc444870056

https://d.docs.live.net/f14659b146ca583e/Thesis/Corrections/Master%20(Repaired).docx#_Toc444870056

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(LC-PBE-D3/6-311++G(d,p)). ....................................................................... 112


(CAM-B3LYP/6-311++G(d,p)). ....................................................................... 113

Table 12. Polynomial fit information for the CP-corrected energy and the 13C isotropic

chemical shift vs the carbon tetrel bond length (MP2/6-311++G(d,p)). ........... 114


chemical shift vs the carbon tetrel bond length (B3LYP/6-311++G(d,p)). ...... 115


chemical shift vs the carbon tetrel bond length (LC-PBE/6-311++G(d,p)). .. 116


chemical shift vs the carbon tetrel bond length (LC-PBE-D3/6-311++G(d,p)).

........................................................................................................................... 117


chemical shift vs the carbon tetrel bond length (CAM-B3LYP/6-311++G(d,p)).

........................................................................................................................... 118


chemical shift vs the carbon tetrel bond length (BHandHLYP/6-311++G(d,p)).

........................................................................................................................... 119

XII

Table 18. CP -corrected energy and the 13C isotropic chemical shift vs the carbon tetrel bond

angle (CAM-B3LYP/6-311++G(d,p)). In all cases the angle was set so that the

oxygen or nitrogen was placed between two methyl hydrogen atoms. ............. 120

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Abstract

Non-covalent bonds are an important class of intermolecular interactions, which

result in the ordering of atoms and molecules on the supramolecular scale. One such type of

interaction is brought about by the bond formation between a region of positive electrostatic

potential (-hole) interacts and a Lewis base. Previously, the halogen bond has been

extensively studied as an example of a -hole interaction, where the halogen atom acts as

the bond donor. Similarly, carbon, and the other tetrel elements can participate in -hole

bonds. This thesis explores the nature of the carbon tetrel bond through the use of

computational chemistry and solid state nuclear magnetic resonance (NMR) spectroscopy.

The results of calculations of interaction energies and NMR parameters are reported

for a series of model compounds exhibiting tetrel bonding from a methyl carbon to the

oxygen and nitrogen atoms in a range of functional groups. The 13C chemical shift (iso) and

the 1cJ(13C,17O/15N) coupling across the tetrel bond are recorded as a function of geometry.

The sensitivity of the NMR parameters to the non-covalent interaction is demonstrated via

an increase in iso and in |1cJ(13C,17O/15N)| as the tetrel bond strengthens. There is no direct

correlation between the NMR trends and the interaction energy curves; the energy minimum

does not appear to correspond to a maximum or minimum chemical shift or J-coupling value.

Gauge-including projector-augmented wave density functional theory (DFT)

calculations of iso are reported for crystals which exhibit tetrel bonding in the solid state.

Experimental iso values for sarcosine, betaine and caffeine and their tetrel-bonded salts

generally corroborate the computational findings. This work offers new insights into tetrel

XIV

bonding and facilitates the incorporation of tetrel bonds as restraints in NMR

crystallographic structure refinement.

XV

Acknowledgements

This work would not have been possible without the help and support of many

friends, family, colleagues and mentors that I’ve worked with over the past couple years.

First and foremost, I would like to thank Professor David L. Bryce, my supervisor, for his

exceptional guidance throughout my time in the Bryce Lab. Thank you for having confidence

in me, and providing me with a rich environment in which I could learn and excel. I look

forward to continuing working with you in the coming years. I would also like to

acknowledge Professors Alain St-Amant and Natalie Goto for reading this thesis and

providing to me valuable comments.

To my friends and colleagues at the University of Ottawa – thank you for your

support and your thoughtful discussions. Dr. Glenn Facey and Dr. Eric Ye at the University

of Ottawa NMR lab, your advice and technical support was invaluable throughout this work.

To my fellow Bryce Lab colleagues, I appreciate our collaboration over the years. Dr. Fred

A. Perras, you first introduced me to solid-state NMR on one of my first days in the lab. I

remember you making me spin up the DOR rotor that day without me knowing anything

about DOR at the time. Nothing could get me more interested in this field on the first day

than getting hands on work. Dr. Kevin M. N. Burgess, while we didn’t work together directly

that much, you taught me to value sober second thought when it came to the more

philosophical aspects of life. Dr. Jasmine Viger-Gravel, you taught me the importance of

being precise and meticulous in my research, a trait you’ve already perfected. To Pat Szell

and Sherif Nour, and more recent fellow graduate students Yijue Xu, Angel Wong, and Peter

Werhun, life in the office and in the lab wouldn’t be as interesting without you. Finally, a

XVI

special thank you needs to be made to Dr. Libor Kobera, who has gone above and beyond in

ensuring I am well trained in the finer aspects of NMR spectroscopy. I would finally also

like to take the opportunity to thank the various undergraduate students who I’ve also worked

with. Jeremy Chin, Michael West and Dylan Errulat, your hard work has produced quality

results.

Of course, all my time couldn’t be spent in the lab alone. I would like to thank my

friends and colleagues in my extended Canadian Armed Forces family for providing me with

an environment in which I could have fun and focus my mind on other things for a while.

Thanks to all of my mentors and supervisors: Maj. Jonathan McAuley, Capt. Dan Parker, the

team at OpsAir, and others whom I’ve worked for directly, for providing me with valuable

mentorship in challenging environments over the years. I believe that today I am a better

leader and your training and support has benefitted me greatly in my civilian life. Thank you

to my colleagues working in support of the Royal Canadian Air Cadets Program for all the

good times; in particular Lt. Alex Schmid, for keeping sane and motivated over the years.

It’s nice to be able to let off steam and vent once in a while! Unfortunately, there are too

many more to mention by name, but you all work so hard in providing an important and

valuable experience for Canadian youth and I’m grateful for your lasting friendships.

Finally, I would like to thank all of my family and relatives for their love and support.

Mom and Dad, over the years you’ve challenged me to go as far as I can in my education,

and you’ve ensured that I could realize my goals without too much trouble. Evan, you’ll have

to deal with that a little longer, but thanks for reminding me not to take anything for granted.

Thank you, Grandpa, in particular for always believing in me, and making me feel like a

“smart cookie”. Jane and Doug, thanks for being family to me when mine was so far away.

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And finally, Alison, you’ve stood by me for everything, and I couldn’t imagine being with

anyone else as I move on to the next chapter of my life. You are the love of my life.

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“I have been looking for

someone to come up with NMR investigations on this interaction,

though, I thought it would be difficult. NMR evidence for hydrogen

bonding came nearly a century later. Tetrel carbon bonding

is barely a few years old.”

Elangannan Arunan

XIX

Statement of Originality

I certify that the work presented in this thesis is my own. With permission from the

publisher, the scientific contribution of this work is based on my own published work in a

peer reviewed journal. Sections 1.4 and 1.5, as well as Chapters 2, 3 and 4 are in part, or

wholly based on the work published in:

Southern, S. A. and Bryce, D. L. NMR Investigations of Noncovalent Carbon Tetrel Bonds.

Computational Assessment and Initial Experimental Observation. The Journal of Physical

Chemistry A, 2015, 119, 11891-11899. DOI: 10.1021/acs.jpca.5b10848.

Chapter 1 – Introduction

1

Chapter 1 - Introduction

1.1 The Basic Properties of Matter

It has been a long time since the idea of the particle first emerged among humans.

The imaginations of the ancient Greek philosophers led them to believe that matter was

not simply made of what could be seen, but rather individual units. Plato first suggested

that matter was essentially divided into polyhedral subunits called elements: earth, air,

water and fire. From that point, the great philosophers argued whether matter was

continuous, or made from discrete units, trying for many years to resolve the issue before

them.

The quest for the answer was later resolved by John Dalton, who first proposed

the idea of atomic theory.1,2 Since then, science has evolved to the point now, where

matter has been almost fully characterized right down to the subatomic level, so far as

even observing the elusive Higg’s boson.3,4

In this tiny world, particles behave much differently than one would expect.

Humans are used to seeing that when a baseball is thrown by the outfielder, it forms an

arc before it arrives at the baseman; this motion is a result of classical mechanics.

However, we must use quantum mechanics to describe the intricate details of the nature

of the subatomic particles; the constituents of the atom.

Atoms are particles which are composed of electrons, neutrons and protons. When

atoms are combined together, they form matter, which can form materials that we are

more familiar with and that we can interact with. The atom can be described as a nucleus

containing the neutrons and protons, surrounded by the orbiting electrons (Figure 1).


2

Figure 1. A basic representation of a 12C atom using the Rutherford-Bohr model. The

nucleus (blue) is surrounded by the orbit of electrons occupying two energy levels. Two

electrons (yellow) reside in the n=1 shell, and four in the n=2 shell. Note that further

electronic orbitals may exist beyond those that are occupied in the case of an excited

electronic state.

The atom is defined by its atomic number, which represents the number of protons

residing within the nucleus. The atomic weight is the average of all the weights of each

isotope, weighted according to their abundance in nature. An isotope of a particular

element is one which has a different number of neutrons than the other.5 For example,

while 12C contains six neutrons and six protons, 13C contains seven neutrons, and six

protons. A given atom that is isolated will always carry the same number of electrons,

regardless of the isotope.

The electron configuration of a particular atom describes the arrangements of its

electrons in terms of discrete atomic orbitals. It assumes that only two electrons may


3

occupy a given atomic orbital, as defined by the Pauli Exclusion Principle.6,7 Closest to

the nucleus is the 1s-orbital. Further away are the p-, d-, and f-orbitals, each with x, y, and

z Cartesian components. Consider a 12C atom, which has six electrons. Its formal

configuration is 1s22s22p2 because it has two electrons in its core orbital, and a total of

four electrons in the valence s- and p-orbitals. It is worth noting that in quantum

mechanics, the square of the atomic orbitals represent the probability of observing

electron density at any point in space surrounding a nucleus, so they exist in various

shapes and symmetries. 7 The larger the atom, the more electrons it has, and therefore the

more orbitals that are filled. Hund’s rule8,9 states that the electronic orbitals are filled with

one electron, before filling it with a second. So when there are three p-orbitals of the same

energy, each must be filled by one electron before they can be filled again by a second

electron. To illustrate this, Figure 2 shows the electronic configuration of fluorine, where

the 2𝑝-orbitals are each filled by one electron, then by a second electron of opposing spin.

The 2𝑝𝑍-orbital remains filled with only one electron.


4

Figure 2. The electronic configuration diagram for a single fluorine atom (1s22s22p5).

The filling of the molecular orbitals, with increasing energy, follows Hund’s rule.

In describing the electronic orbitals as a set of allowed states which the electrons

can possess, they can be quantized by the quantum number, n. By doing this, the idea of

quantum mechanics is introduced to the description of the atom. Quantum mechanics is

the more accurate description and it will be used throughout this thesis.

Protons have a net positive charge, and electrons hold negative charge. However,

this is a simplistic view of the particle, and in fact, their character becomes more complex.

In fact, the description of subatomic particles may include such characteristics as spin,

angular momentum, and magnetic moment.

Nuclear spin is an important property of the nucleus. Just as the Earth rotates

around its axis, spin can be thought of, in a classical sense, as the rotation of a nucleus

around its own axis.10 Consequently, particles possess spin angular momentum. Consider

a gyroscope. When it is spun, it tends to remain in place until a force is acted upon it due


5

to the conservation of angular momentum. While it may seem quite familiar, this classical

description of the elementary particle is, of course, false, and indeed nuclei do not actually

rotate around axes in the way a planet does. Instead, chemists resort to quantum

mechanics in order to properly describe the angular momentum due to the fact that

subatomic particles display properties of both particles and waves (the wave-particle

duality). Spin is an intrinsic property10, and it may be described as α or β; being “up” or

“down,” respectively. They are represented in the electronic configuration diagrams by

upward and downward arrows, respectively (Figure 2).

1.2 Noncovalent interactions

Noncovalent interactions are the result of the interactions between electrons

resulting from their charge distributions over a particular atom or molecule. These

interactions can, consequently, exist between two different molecules or within a

molecule but between nearby groups. Some examples of noncovalent interactions include

van der Waals (vdW) interactions, 𝜋-interactions and electrostatic interactions.

Electrostatic interactions, such as the dipole-dipole interaction is an example of

an attractive vdW interaction arising due to the electronic dipoles formed from the

asymmetric distribution of electrons over the surface of an atom or a molecule, where

some regions tend to be more electronegative than others.5 In some cases, that region may

also possess a formal charge. For example, two molecules of acetone may interact

between the carbonyl oxygen of one molecule and the carbonyl carbon of the other.

Hydrogen bonds exhibit partially noncovalent character (Figure 3), whereby the partially


6

positive charge on the hydrogen atoms can interact with a partially negative charge.11,12

𝜋-interactions may, for example, occur between the negative charge distribution on

aromatic faces resulting from the 𝜋-orbitals, and any partially positive or formally

positive counter charge, such as an ion or another aromatic ring. These interactions are

quite weak, on the order of less than 10 kcal/mol, yet significant especially in protein

folding or molecular signalling, because amino acids histidine, tryptophan,

phenylalanine, and tyrosine all contain aromatic rings with 𝜋-systems.13,14

Figure 3. The hydrogen bond. The electrostatic interactions between the partially positive

(δ+) and partially negative (δ-) charge contribute to an attractive interaction between the

oxygen and hydrogen atoms in water molecules.

Noncovalent bonding mediated by -holes has been studied extensively in the

context of halogen bonding15,23,24, pnicogen bonding 16,17, chalcogen bonding. 18,19,20,21

Bonding involving the noble gases, coined “aerogen bonding”, has also been explored in

the recent years. 22 Halogen bonding23,24 is an example of a noncovalent interaction, where


7

an area of partially positive charge, called a 𝜎-hole25,26, acts as an electrophile for a

negatively charged or electron rich molecule.

Each of the preceding are examples of hole interactions which is a subclass of

noncovalent interactions.27,28 In every case, the bond donors interact with a Lewis base

like entity, such as electronegative atoms or lone pairs of electrons (Figure 5). As with

covalent bonds, the strength of the hole bond can be expressed in terms of energy,

whereby the resulting energy is known as the bonding energy.

Table 1. Typical interaction strength of noncovalent interactions compared to some

examples of covalent bonds. A variety of examples were selected to present an idea of

expected interaction energy strengths.

Interaction

Interaction Strength

/ kcal mol-1

Covalent Bond C-C 8529

C-H 10029

C=O 17529

Hydrogen Bond 1-329

PHN 0.830

van der Waals Interactions 0.5-129

Halogen Bond 1-731

chloro-cyanoacetylene 2.332

Chalcogen Bond H2SCl- 0.8133

SCSCl- 10.5933

F4SNH3 1421

Pnicogen Bond FNN 430

PNN 730

F4PNH3 4317

H3FPNH3 3617


8

1.2.1 Sigma-Holes

Computational examination of the electrostatic potential (ESP) surfaces of

halogen bonding molecules revealed that on one side of the interaction, there was an area

in which different charges were present on a single atom.25,26

Consider a symmetric atom in a vacuum in the absence of any external effect of

charge, magnetism or other influences. In the case of this lone atom, the ESP is generally

positive because the effect of the nucleus dominates over the effect of the electrons which

are dispersed over the entire atom.34 The electrostatic potential resulting from the

contributions of the electron density, 𝜌(𝑟), and the charge on the nucleus, 𝑍𝐴, at any point

𝑟 on the surface of an atom is given by34:

𝑉(𝑟) = ∑𝑍𝐴

|𝑅𝐴 − 𝑟|− ∫

𝜌(𝑟′)𝑑𝑟′

|𝑟′ − 𝑟|𝐴

1

where the distance between the point and the nucleus is 𝑅𝐴. Typically, the 𝜌(𝑟) =

0.001 electrons/bohr3 surface is used to represent a molecular surface, corresponding to

an electrostatic potential of 𝑉𝑠(𝑟). When the effects of the electrons dominate at a given

point, the expression yields a negative value on the potential surface. The ESP provides

an effective and convenient way to model the σ-hole in noncovalent bonding.26

The σ-hole is an area at which 𝑉(𝑟) has a value that is more positive than the

surrounding area, thus indicating and area of electronic depletion. When the atom of

interest is covalently bound to another atom or functional group with electron

withdrawing character, such as a trifluoromethane group, a substituted aromatic ring, an

amino group, the tendency is for the electronic distribution to be drawn toward the


9

covalent bond. This gives rise to a hole situated along the extension of the covalent

on the opposite side of the atom of interest. The point representing the hole can be

depicted as 𝑉𝑠,𝑚𝑎𝑥 because it typically portrays a local area of maximum electrostatic

depletion.15

The electrostatic depletion at 𝑉𝑠,𝑚𝑎𝑥 can be explained using natural bond order

(NBO) analysis.35 It has been shown that the halogen bond donor atoms tend to possess a

sigma bonding orbital as well as three unshared pairs of electrons, each occupying the p-

orbitals. The 𝑝𝑧 orbital lying along the axis of the covalent bond is half filled, resulting

in an 𝑠2𝑝𝑥2𝑝𝑦

2𝑝𝑧1 character. The result is therefore a “belt”35 of negative electrostatic

potential around the halogen atom, leaving an area of electronic deficiency on the

opposite end of the covalent bond; the hole.26 The magnitude of this electronic

deficiency comes down to the amount of s character is present in the p-orbital; the more

purely p the orbital is, the stronger the hole.26 The hole can be effectively neutralized

by a negative group such lone pair of electrons, and this accounts for the high degree of

linearity in such an interaction.36 The situation is somewhat different with respect to the

group IV tetrel elements. The tetrel elements do not have lone pairs of electrons, and are

as such sp3 hybridized. Consequently, there is a large amount of s-character in the bonding

orbitals. The conclusion is, however, that reduced p-character of the bonding orbital is

acceptable, and the hole remains present, albeit weaker.36


10

Figure 4. The electrostatic potential at the 0.001 a.u. surface of various structures

exhibiting σ-holes. The σ-hole is present on (b) chloromethane; (c) fluoromethane; (d) a

methyl group that is covalently bonded to methylammonium. For illustration purposes, a

molecule of methane (a) is shown and does not to possess a sigma hole on carbon. Instead,

the area where the hole ought to be is more negative due to the electronic depletion

over the hydrogen atoms (each of which coincidently possess a single hole15). The red

colour corresponds to electrostatic potential values ≤ 0.172 a.u. and the blue colour

corresponds to electrostatic potential values ≥ 0.179 a.u.

The strength of a σ-hole depends significantly on the electron withdrawing

character of its covalently bonded partner atom or molecule.36 Considering iodine, bound

to a methyl group, one is not likely to observe a significant hole. In this case, the methyl

carbon is not considered to be very polarizing because the hydrogen atoms do not have

any polarization capabilities. In fact, the polarization strength of iodine has a greater effect

and it would be more likely that a negative hole would be found on the iodine atom,

and a positive hole on the carbon. 26 Conversely, when fluorine atoms, or other


11

electron-withdrawing substituents such as aromatic rings, are substituted for the hydrogen

atoms, a relatively strong hole is introduced as a result of the increased electron

withdrawing ability of the other group.26.19

The electronic potential of a number of holes generated by various electron

withdrawing substituents has been listed by Politzer et al.27 They show that the strongest

holes are achieved when cyanide groups are used, although these holes are achieved

only when the entire isoelectric surface is positive in nature. Other substituents, such as

fluorine and chlorine, also contribute to the formation of holes.15 in general, 𝑉𝑠,𝑚𝑎𝑥

becomes increasingly positive as the rest of the molecule becomes more electron-

withdrawing.37

1.2.2 Sigma Hole Bonding

Consider a molecule or fragment RX interacting with a nucleophilic molecule or

fragment Y (often an anion, a Lewis base, or -electrons). The -hole is on X along the

extension of the covalent bond to R (Figure 5). Depending on the identity of element X,

such interactions take on their own names in the literature, e.g., halogen bonding,

pnicogen bonding, chalcogen bonding, and aerogen bonding, where the name of the

interaction refers to the periodic table group to which the bond donor (electron acceptor)

belongs (group V: pnicogens; group VI: chalcogens, etc.).38 These are all different types

of -hole bonds.


12

Figure 5. General schematic of a tetrel bond, where R is a covalently bonded atom or

functional group, X is the tetrel bond donor (X = C, Si, Ge, Sn, or Pb), and Y is the tetrel

bond acceptor.40 dX-Y is smaller than the sum of the van der Waals radii of the interacting

atoms.

The hole has been studied extensively as it applies to halogen bonding.

Considering again the iodine atom covalently bound in I-CF3, one would expect to

observe a relatively significant hole. In terms of its electropositive character, the

magnitude of 𝑉𝑠,𝑚𝑎𝑥 within the hole increases as the atomic number of the halogen

increases, thereby increasing the interaction strength of the halogen bond.15 For example,

the hole bond between a -electron and an iodine atom would be greater than that

resulting from a bromine atom.

In general, the bonding energy is a negative value, representing an attractive

interaction. The correlation between the 𝑉𝑠,𝑚𝑎𝑥 and the interaction energy is such that

when the electronic depletion on the hole is increased, the magnitude of the bond

strength increases as well. It can therefore be expected that bond donors with higher

atomic numbers will more readily form bonding interactions. That’s not to say that


13

weakly polarized atoms such as carbon will not participate in these types of bonds; the

bonds will simply be weaker in nature and sometimes difficult to produce by

crystallization.

1.3 Group IV “Tetrel” Bonding

The focus of this thesis is on tetrel bonding, named after the bond donor, which falls under

group IV in the periodic table.36,39,40,56 In an R-C···Y carbon tetrel bond (Figure 5), the

-hole resides on carbon. As noted by Politzer27, often in such group IV cases, all or

almost all of the electrostatic potential on the R-C moiety is positive and in such cases the

-hole is simply identified as a region which is more positive than its surroundings

(Figure 4), leading to the preferential formation of an interaction from the -hole over

other types of complexes.

As is generally the case for -hole bonds, the strength of the tetrel bond depends

largely on the atomic number of X and by the electron withdrawing ability of the R

substituents.41,42,43 The nature of the tetrel bond donor has an impact on the tetrel bond

strength, whereas the atomic size of the bond donor increases from C to Sn, the bonding

energy increases. This is attributed to an increase in the polarizability of the atom as one

goes down the periodic table, thus increases the size of the hole.


14

Figure 6. (a) The electrostatic potential at the 0.001 au surface of positively charged

dimethylammonium (left) and formaldehyde (centre) computed by CAM-B3LYP/6-

311++G(d,p). The red colour on dimethylammonium (right) corresponds to electrostatic

potential values ≤ 0.172 au; the blue colour corresponds to electrostatic potential values

≥ 0.179 au. The -hole is present on the methyl carbon and is adjacent to the C-N -bond,

and it has an electrostatic potential value of 0.179 au. (b) A carbon tetrel bond involving

a methyl carbon. (c) An example of a carbon tetrel bond occurring in the crystal structure

of sarcosinium tartrate.44

Experimental evidence for tetrel bonding involving Si and Sn has been in the

literature for many years. Silicon tetrel bonding was noted to mediate chemical reactions

by its hexacoordinated intermediate.45 In other cases, hexacoordinated tetrel bonded

silicon atoms have been observed to exist in various species. 46,47 Inter- and

intramolecular tetrel bonding of silicon and lead atoms have also been demonstrated

through crystallographic methods.48,49,50


15

Additional evidence for the existence of tetrel bonding involving carbon as well

as silicon has been growing significantly in recent years.36,39,51,52 Quantum calculations

have confirmed the presence of carbon tetrel bonds between electron deficient carbon

atoms and electron rich tetrel bond acceptors.40,42,53,54 The importance of the tetrel bond

may be analogous to other forms of noncovalent bonding. Given that carbon atoms are in

abundance in nature and in synthetic chemistry, carbon tetrel bonding may play important

roles in the organization of molecular units, from natural products to functional materials

and pharmaceuticals. Furthermore, it could be envisaged that carbon tetrel bonding could

play a role in directing molecular orientation in some dynamic systems, such as protein

folding, ligand-acceptor interactions, or other processes of biological importance.40,55 For

instance, it has recently been suggested that the carbon tetrel bond could play a critical

role in directing SN2 reactions (Figure 7).56 A search of the Crystal Structure Database

(CSD) demonstrates that there are perhaps thousands of examples where the tetrel bond

interactions exist, and could be contributing to the three-dimensional packing

arrangements of molecules within their crystal lattices.

Figure 7. A schematic showing the influence of a tetrel bond on the activation of an SN2

reaction. Inspired from the work of Grabowski.56 Purple: fluorine; Grey: carbon; White:

hydrogen; and Yellow: chlorine.


16

Recently, Arunan related the atoms in molecules (AIM) descriptors for a hydrogen

bond57 to the carbon tetrel bond, an implication that similar rules could be applied to tetrel

bonding.15 These criteria are meant to test for the presence of a bond path indicative of a

noncovalent interaction (a hydrogen bond in the original paper). Among these criteria

were: 1. A bond path linking two interacting atoms must connect the bond critical point

which is present between both atoms; 2. There must be mutual penetration of the electron

density clouds; 3. On the formation of the complex, the bond donor loses some charge,

and there is some destabilization on the donor atom; 4. The atomic volume of the donor

atom decreases. In almost all of the examples presented by Arunan, the carbon tetrel

bonded complexes follow the proposed behaviour of hydrogen bonds.

IR spectroscopic studies on tetrel bonded complexes have shown that there is a

red shift in the C-X stretching frequency due to hyperconjugation of lone pair orbitals of

the bond acceptor and the anti-bonding orbital of the bond donor.15 This causes a

weakening of the sigma bond between X and C causing a decrease in the stretching

frequency.

Finally, computational work in 2009 provided key evidence predicting -hole

bonding to the lightest tetrel element, carbon.36 More recently, Thomas et al. identified

716 compounds which may exhibit C···O tetrel bonding in the compounds in the CSD.58

They conducted important experiments providing charge density analysis of fenobam and

dimethylammonium 4-hydroxybenzoic acid in the solid state, each exhibiting carbon

tetrel bonds. The results indicated the presence of a tetrel bond on the latter structure.


17

However, the former preferentially formed hydrogen bonds between the methyl hydrogen

and the associated chlorine atom.

1.4 Nuclear Magnetic Resonance Spectroscopy

1.4.1 The Zeeman Interaction

It is useful to begin the discussion of nuclear magnetic resonance (NMR) by first

discussing the basics of quantum mechanics. Nuclei possess a nuclear spin quantum

number, 𝐼, which can take the values of integers and half integers of 0, ½, 1, etc.,

increasing in intervals of one half. Nuclei possessing spin with integer values of 𝐼 are

known as bosons while nuclei with half-integer spin values are called fermions.10

Related to spin is the property called angular momentum, 𝐿, given by eqn. 2 as:10

𝐿 = ℏ√𝐼(𝐼 + 1) 2

The nuclear spin angular momentum is a vector with a component along the z-axis. The

z-component interacts directly with the applied magnetic field, 𝐵0 (reported in units of

Tesla (T)), which also lies along the z-axis. It is for this reason that the angular momentum

operator representing its z-component can therefore be defined by 𝐼𝑧.

The angular momentum gives rise to an intrinsic property called magnetic

moment, 𝜇, representing the interaction between the nucleus and the magnetic field.10 𝜇

is dependent on both the nuclear spin angular momentum and the gyromagnetic ratio, 𝛾

(rad s-1 T-1). The total energy from this interaction is given by:59


18

𝐸 = −𝜇𝐵0 3

The spin quantum number, 𝐼, has corresponding eigenvalues of 𝑚𝑙, equal to – 𝐼 to

+𝐼 in intervals of 1. Thus, for any value of 𝐼, there are precisely (2𝐼 + 1) eigenvalues.

The 𝐼𝑧 operator has (2𝐼 + 1) eigenfunctions. In general, this can be represented by:

𝐼𝑧𝜓𝑚 = 𝑚𝑙ℏ𝜓𝑚 4

It is now useful to define the Hamiltonian for a spin in a magnetic field. The

Hamiltonian operator is dependent on the gyromagnetic ratio, 𝐵0, and the angular

momentum operator. Eqn. 5 describes the Hamiltonian:

�̂� = −𝛾𝐵0𝐼𝑧 5

Thus, when the Schrödinger equation for a single spin in the magnetic field is

given by:

�̂�𝜓𝑚 = 𝐸𝑚𝜓𝑚 6

where the energy, 𝐸𝑚 (in units of Joules) representing the eigenstates of the nuclear spin

in the presence of the magnetic field is given by eqn. 7:

𝐸 = −𝑚𝑙ℏ𝛾𝐵0 7

Each energy state can be labelled as an α state or a β state, representing the lower

energy and higher energy levels, respectively. These eigenstates are related to the


19

magnetic moment such that lowest possible energy is brought about by perfect alignment

with the magnetic field. The transition energy corresponds to the energy which must be

subjected to a nuclear spin in order to induce a transition from the α state to the

corresponding β state, matching to a specific electromagnetic frequency. This is referred

to as the NMR transition, and the transition can only occur when the difference between

both values of 𝑚𝑙 is equal to exactly one. The frequency of the photon that will induce an

NMR transition, or the Zeeman Effect (Figure 8), is given in eqn. 8, where 𝜈0 is the

Larmor frequency, and is isotopically specific due to its dependence on the gyromagnetic

ratio.

𝜈0 =𝛾𝐵0

2𝜋 8

In a simple system, one would expect a line on the NMR spectrum at the exact

frequency of 𝜈0. However, this is not typically the case because nuclear spins are usually

affected by their chemical environments. The energy eigenvalue becomes significantly

more complex as the nature of the nearby electrons, as well as the coupling to other nuclei

is taken into account.


20

Figure 8. The Zeeman Effect for a spin 1

2 nuclide. The splitting of the spin states is

observed as a function of the strength of the magnetic field.

In the absence of a magnetic field, the direction of the spins is isotropic.10 When

a sample is placed in 𝐵0, the interaction of the spin nuclear magnetic moments with the

magnetic field will cause their bulk alignment with 𝐵0. This is a process that is time

dependent and is known as 𝑇1 spin-lattice relaxation. The net equilibrium magnetization

can be represented by the vector, �⃑⃑⃑� . In the end, the spin polarization does not align with

the magnetic field per se, but instead, the magnetic moments cause the spins to rotate

around 𝐵0 in the shape of a “precession cone”10 with oscillations equal to 𝜈0. The z-

component of the magnetization is important for NMR.

At the thermal equilibrium, the distribution of spins in the high energy state versus

the low energy state is governed by the Boltzmann distribution:


21

𝑛𝛼2

𝑛𝛽1= 𝑒−

Δ𝐸𝑘𝑇 9

The NMR experiment is therefore the practice of manipulating the magnetization

vector through space. A sample is placed in a coil which is situated in the xy-plane

perpendicular to 𝐵0. By applying a radiofrequency (RF) pulse along the x- or y- axis, the

magnetization may be tilted away from the z-axis. In doing so, the magnetization

precesses around the z-axis at the Larmor frequency, resulting in a component of the

vector oscillating in the xy plane. The vector oscillations can be detected as it induces a

current in the coil. These oscillations are detected by the spectrometer. The magnetization

vector continues to precess around the z-axis, but the cone eventually returns to the

thermal equilibrium along the z-axis, causing a gradual decrease of the xy component of

the magnetization over time. The detected current in the coil resulting from the

oscillations in the xy-plane is known as the free induction decay (FID). The FID is

transformed from the time domain to the frequency domain through Fourier transform to

an NMR spectrum.

As it was mentioned before, nuclear spins are affected by their chemical

environments. For example, the effects of the electrons shielding the interaction between

the nucleus and 𝐵0 would have a direct effect on the resulting NMR transition. Other

effects, such as spin-spin coupling, or the quadrupolar interaction of some nuclides can

have a major impact on the NMR spectrum. These NMR interactions are essentially

perturbations to the Zeeman interaction. Thus, the NMR spectrum is complicated by the

fact that these interactions exist.


22

The Hamiltonian for a spin in a magnetic field is therefore not only dependent on

the Zeeman Hamiltonian alone (eqn. 5). In fact, it is additionally dependent on the

magnetic shielding interaction, the direct and indirect dipolar coupling interactions, and

the quadrupolar interaction in the case of nuclides with spin greater than 1

2. It is therefore

essential to examine some of these interactions in detail. For the purposes of this thesis,

only the magnetic shielding interaction as well as the indirect spin-spin J-coupling

interactions will be discussed in detail.

1.4.2 Magnetic Shielding

Magnetic shielding is brought about by the magnetic fields generated by the

electrons. These fields may be additive or subtractive to 𝐵0, and consequently change the

way the nuclear magnetic moment interacts with the magnetic field. The magnetic field

seen by the nucleus as a result of the effects of magnetic shielding is given by:

𝐵𝜎 = (1 − 𝜎)𝐵0 10

where 𝜎 is the shielding constant.

Using the secular approximation, the magnetic shielding operator is shown in eqn.

11 to be dependent on the gyromagnetic ratio and the shielding constant.

�̂�𝜎 = −𝛾ℏ𝜎𝐵0𝐼𝑍 11


23

The magnetic shielding interaction is anisotropic by nature, meaning it is

orientationally dependent. In expression 12, the magnetic shielding tensor is diagonalized

such that the interaction is represented by its principal axis system (PAS).

[

𝜎𝑥𝑥 𝜎𝑥𝑦 𝜎𝑥𝑧

𝜎𝑦𝑥 𝜎𝑦𝑦 𝜎𝑦𝑧

𝜎𝑧𝑥 𝜎𝑧𝑦 𝜎𝑧𝑧

] ⇒ [

𝜎11 0 00 𝜎22 00 0 𝜎33

] , 𝜎11 ≤ 𝜎22 ≤ 𝜎33 12

The isotropic shielding constant, 𝜎𝑖𝑠𝑜, is given as the average of the three shielding

tensor components (eqn. 13). Further parameters which may be used are the span, Ω, and

the skew, κ, measuring the breadth of the signal and the asymmetry, respectively (eqn. 14

and 15).60 The span is related to the distribution of the signals corresponding to the

orientations the molecule takes in the sample, which is averaged out in a solution, and the

skew is the asymmetry of the distribution of the signals.

𝜎𝑖𝑠𝑜 =𝜎11 + 𝜎22 + 𝜎33

3 13

Ω = 𝜎33 − 𝜎11 14

κ =3(𝜎𝑖𝑠𝑜 − 𝜎22)

Ω

15

The shielding constant is observed directly in the NMR spectrum in the form of a

chemical shift. The chemical shift is the value of 𝜎 with respect to a reference. For

example, the secondary reference for a 13C spectrum could be glycine, and the chemical

shift of the carbonyl carbon is 176.4 ppm with respect to tetramethylsilane (𝛿𝑖𝑠𝑜TMS =

0 ppm).61 In units of Hz, the chemical shift is defined by eqn. 16:


24

𝛿 =𝜎𝑟𝑒𝑓 − 𝜎

1 − 𝜎𝑟𝑒𝑓 16

The preceding formula can also give the chemical shift in units of parts per million

by simply multiplying by 106.

1.4.3 Spin-spin coupling

In general, coupling results from the interaction between two different spins.

Indirect spin-orbit coupling (J-coupling) occurs when the interaction between two nuclear

spins is mediated by the electrons involved in their bonding.

J-coupling is typically only a very small perturbation to the Zeeman interaction.

Therefore, it is likely that the other NMR interactions overshadow the presence of this

interaction because it tends to be on the order of a few Hz for first-row elements.

Nevertheless, J-coupling is a very important tool for probing the connectivity of atoms in

a molecule.62 In units of Hz, the J-coupling operator between nucleus 1 and 2 is:

�̂� = 2𝜋𝐼1𝐽𝐼2 17

In the preceding Hamiltonian, 𝐽 is the orientation-dependent J-coupling tensor.

The isotropic J-coupling (𝐽𝑖𝑠𝑜) is the average of the principal components of the tensor.

The anisotropic contribution to J-coupling (Δ𝐽) is averaged out in the molecular tumbling

of an isotropic solution. However, in the solid state, it remains present, albeit often small.

The sign of 𝐽𝑖𝑠𝑜 is dependent on the gyromagnetic ratios of each of the spins for the case

of single bonds.


25

Ramsey’s theory63 states that there are precisely five mechanisms that contribute

to the total J-coupling. Fermi contact (FC) is typically the dominant contribution to J-

coupling. It is important to recall that s-orbitals have electron density at the nucleus. The

FC contribution arises due to the interaction of the electronic spins and the nuclear spins

when the electronic density is at the nucleus. Therefore, the FC contribution is typically

a good indicator of chemical bonding. The paramagnetic spin orbit (PSO) and the

diamagnetic spin orbital (DSO) mechanisms emerge due to the coupling of angular

momenta of the electrons around two nuclear spins. The spin dipole (SD) term is simply

due to the coupling between the nuclear and the electronic spins. Finally, there exists a

(FC × SD) cross term which is usually a major contribution Δ𝐽. It is important to note that

the FC mechanism does not contribute to Δ𝐽.64

1.4.4 Other NMR interactions

Other contributions to the total nuclear spin Hamiltonian which arise due to the

interaction with a magnetic field are dipolar coupling and quadrupolar coupling. Direct

dipolar coupling is a case of nuclear spin coupling, but in this case it is a result of the

interaction of the two magnetic dipoles resulting from the magnetic moments of each of

the nuclei. It is a through space interaction, as opposed to J-coupling, which is a through-

bond interaction mediated by interceding electrons. Accordingly, dipolar coupling can be

used to measure the distance between nuclei or give global snapshots of macromolecules.

65,66


26

The quadrupolar interaction affects nuclei that have spin greater than 1

2.10 The

quadrupolar interaction arises because these nuclei have a non-spherical distribution of

charge within the nucleus. This distribution is expressed as the quadrupole moment, 𝑄,

which couples with the electric field gradient (EFG) caused by the nuclei and electrons

within the molecule. This interaction is often very strong, so the quadrupolar interaction

usually dominates the NMR spectra of quadrupolar nuclides.

Using all of the preceding NMR interactions, it possible to obtain a substantial

amount of information about the electronic structure of a molecule. This is the power of

solid-state NMR spectroscopy; it is a tool that has the potential to reveal a lot of

information that can lead to conclusions about the nature of molecular systems. In this

work, solid state NMR is used to reveal the nature of noncovalent chemical bonding

between atoms.

1.5 Objectives

It is clear that noncovalent bonds play important roles in every aspect of life and

chemistry. It is therefore extremely important to fully understand how they work so as to

develop more efficient strategies for dealing with the molecular chemistry and properties

of materials.

Previously, there has been only limited analysis of -hole bonds involving the

Group IV “tetrel” elements. Tetrel bonds with carbon acting as the bond donor are

considered to be of great importance since carbon atoms are greatly abundant in nature


27

and in chemistry. Therefore, further research into the area of tetrel bonding is extremely

important.

Nuclear magnetic resonance (NMR) spectroscopy is an important tool for

furthering the understanding of noncovalent interactions. Work on halogen bonds, using

both experimental and computational methods, has demonstrated the sensitivities of

chemical shifts, quadrupolar couplings, and J-couplings to the halogen bond geometry in

crystalline materials.67,68,69,70,71 In methyl tetrel bonds, it has been shown that the methyl

hydrogens surrounding the tetrel bond experience a decrease in their chemical shifts.72

The major goal of this thesis is to determine whether the presence or the absence

of a tetrel bond can be detected using solid-state NMR. In the present study, investigations

into carbon tetrel bonding are expanded using NMR quantum chemical calculations and

solid-state NMR spectroscopy with the goal of observing how the presence of carbon

tetrel bonds, and their geometries, may affect the NMR response. The NMR parameters

observed are chemical shifts, providing an indication of the magnetic shielding on the

tetrel atom, and the computed J-coupling, giving insights to the connectivity of the tetrel

bond.

Chapter 2 – Instrumentation and Methodology

28

Chapter 2 - Instrumentation and Methodology

2.1 Sample Preparation

2.1.1 Introduction to Theoretical Aspects of Powder X-Ray Diffraction

The work of this thesis was complemented by an analytical technique known as

powder X-ray diffraction (PXRD). Specifically, the identities of the synthesized crystals

were confirmed by PXRD as it allows for crystal structural determination using powdered

samples. In comparison to single crystal X-ray diffraction, PXRD can be more efficient as it

avoids the need for growing single crystals, which can be a long, sometimes laborious, and

often costly endeavour.

It has certainly been possible, while not very trivial, to solve ab initio a crystal

structure using PXRD.73,74,75 In this work, rather than solving the crystal structure, PXRD

results are compared to known data to verify the correct product has been produced.

In PXRD, the sample is bombarded with X-rays from angles set by the user. The

range of angles depends entirely on the sample since the signals generated from the X-ray

diffraction on the diffractogram are obtained as a function of the angle. In many cases, no

diffraction pattern past the angle of 65 degrees may be obtained, while with other samples,

the range may be larger or smaller. The peaks in the diffractogram depend ultimately on the

crystal structure of the compound.

First, the sample is spread onto a sample plate made of either glass or some metal. It

is then placed in the X-ray diffractometer, which consists of a cathode ray tube that generates

X-rays. The resulting X-rays are passed through a monochromator in order to filter out

unwanted wavelengths of electromagnetic radiation. The X-rays then make contact with the


29

surface of the material, and are either scattered by the atoms in the sample, or passed to the

next layer of atoms to either scatter or pass through again. Constructive interference occurs

when the X-ray beams from two different layers are in phase. This is detected and shown as

a peak on the diffractogram. This process follows Bragg’s Law:

𝑛𝜆 = 2𝑑 sin 𝜃 18

where 𝜆 is the wavelength, 𝑑 is the spacing between the layers, and 𝜃 is the incident angle

of the X-ray beam. The detector accepts the X-rays at an angle of 2𝜃 from the cathode ray

tube as both rotate around the sample, and the diffraction pattern is hence reported as a

function of 2𝜃 on the diffractogram. This is known as the Bragg-Brentano method.

2.2 Quantum Computational Chemistry

2.2.1 The Hartree-Fock Method and the Self Consistent Field

Quantum computational methods allow chemists to study complex systems existing

with more than one electron in order to understand its fundamental properties. Ab initio

methods have enabled the calculation of the electronic information of complicated systems,

which gives researchers better insights into the intricate details of their study. In many fields,

quantum computational methods allow for the de novo discovery of the properties of various

materials which cannot be studied alternatively. However, in this work, quantum chemical

computing is used as a means to complement the findings of experimental studies in order to

achieve a greater confidence to the solution of a given problem.


30

In order to successfully employ quantum chemistry, it is important to properly

understand the basics of how it works. It is often the case that a person will use a tool at their

disposal but it is not always that the user knows how that tool works. In order to fully

appreciate the power of quantum computational chemistry, the fundamentals aspects must

be understood.

The electronic structure of a system can be described by the solution to the time

independent Schrödinger equation. The solution to the Schrödinger equation can be entirely

independent of any experimental information, making it a first principles method. Solving

the electronic structure is, however, a very difficult task. Except for the case of a single, and

sometimes even a dual electron system, it is not computationally feasible to obtain the exact

solution. Ab initio methods usually always employ some sort of technique to solving the

Schrödinger equation through various simplifications and approximations, and therefore

allow for very close estimations of the true solution, but not necessarily the solution itself.

The time independent Schrödinger equation for a ground state system is:

�̂�Ψ0 = 𝐸0Ψ0 19

where the wavefunction describing the spatial distribution of the electronic orbitals is the

eigenfunction for the Hamiltonian operator. The ground state energy is returned as the

eigenvalue of the wavefunction.

The Hamiltonian operator incorporates a number of terms representing both the

kinetic and potential energy of the system.76 In the simplest of cases, these terms include the

kinetic energy of the electrons, the kinetic energy of the nuclei, the attractive electrostatic

interaction between the electrons and nuclei, the repulsive electrostatic interaction between


31

electrons and electrons, and the repulsive electrostatic interaction between nuclei. For 𝑀

nuclei and N electrons, the Hamiltonian operator is thus given by (in atomic units)76:

�̂� = −∑∇𝑖

2

2− ∑

∇𝐴2

2𝑀𝑎+ ∑ ∑

𝑍𝐴

𝑟𝑖𝐴

𝑀

𝐴=1

𝑁

𝑖=1

𝑀

𝑖=1

+ ∑∑1

𝑟𝑖𝑗

𝑁

𝑗>𝑖

𝑁

𝑖=1

+ ∑ ∑𝑍𝐴𝑍𝐵

𝑟𝐴𝐵

𝑀

𝐵>𝐴

𝑀

𝐴=1

𝑁

𝑖=1

20

where 𝑍 is the charge on a given nucleus, and 𝑟 is the distance between two given particles.

It is possible to see that in the preceding expression, when a greater quantity of nuclei

and electrons that are present in the system, the problem becomes extremely complicated. It

is for this reason that the Schrödinger equation for relatively large systems cannot be solved.

In order to overcome this critical challenge, the Born-Oppenheimer approximation is

applied.77 Some assumptions inherent in the Born-Oppenheimer approximation are: 1. there

is a high ratio of electrons present compared to the number of nuclei; and 2. That an electron

is several orders of magnitude less massive than a nucleus. In general, this approximation

means that electrons have the ability to change their position instantaneously with respect to

the relatively slow motion of the nuclei. This assumption effectively separates the electronic

motion from the nuclear motion and considerably simplifies the Schrödinger equation by

only incorporating the electronic terms.

While the electronic Hamiltonian appears to be simpler (and, indeed, it is), the

wavefunction still cannot be solved for molecules or atoms with more than two electrons.

However, it does form the basis for employing various principles and computational methods

for solving the electronic structure as an approximation to the true solution for the ground

state of a system.


32

A key principle that must be considered while attempting to solve the Schrödinger

equation is called the variation principle.76 The variation principle states that the energy

corresponding to any trial wave function, Ψ1, will be greater than or equal to the true ground

state energy of the system. By using the variation principle, it is possible to start with a known

trial wave function, and iteratively minimize the energy such that the resulting trial wave

function resembles the true wave function as much as possible. The energy expression can

then be parameterized by a value of 𝜆, where the trial energy is calculated for each value of

𝜆. The lowest energy obtained is assumed to be closest to the true energy, satisfying the

convergence requirement.

Hartree-Fock (HF) theory was introduced as a means of solving the Schrödinger

equation using simplified wavefunctions to estimate the true energy eigenvalue of any

system with 𝑁 number of electrons. HF theory is a computationally feasible system because

rather than each electron feeling the Coulombic repulsion of every other electron

individually, it essentially considers only the average repulsion felt by a single electron over

the total field of all of the other electrons in the molecule.

It is possible to separate the Hamiltonian in terms of a product of all of the individual

electrons. In order to do this while satisfying the necessary antisymmetric property of the

wave function, a Slater determinant is used. Spin orbitals are introduced when the spin of

each atom is considered. The spin orbital depends on both spatial coordinates as well as the

spin quantum number, 𝑚𝑠. The spin orbitals are all represented by the four coordinate vector

𝐱. As previously mentioned, a spin can have two states, 𝛼 or 𝛽. The spin orbital is represented

by 𝜒𝑖(𝐱𝑖), for each electron, 𝑖. The antisymmetry of the wavefunction can be satisfied if the

wavefunction is expressed in terms of a Slater determinant78, where the spin orbitals and the


33

electronic coordinates are represented in the columns and rows, respectively. The Slater

determinant provides a wavefunction that is antisymmetric, meaning the electrons cannot

occupy the same state. Eqn. 21 shows the Slater determinant representing the Hartree-Fock

wavefunction.

Ψ(𝐱1, 𝐱2, … , 𝐱𝑁) =1

√𝑁![

𝜒1(𝐱1) 𝜒2(𝐱1) ⋯ 𝜒𝑁(𝐱1)𝜒1(𝐱2) 𝜒2(𝐱2) ⋯ 𝜒𝑁(𝐱2)

⋮ ⋮ ⋱ ⋮𝜒1(𝐱𝑁) 𝜒2(𝐱𝑁) ⋯ 𝜒𝑁(𝐱𝑁)

] 21

The HF energy can now be solved in terms of the molecular orbitals in the Slater

determinant. The wavefunction represented by the Slater determinant which has the lowest

possible energy, according to the variation principle, is the wavefunction that most closely

resembles the true wavefunction. In order to obtain the lowest energy Slater orbital, the

variation principle must also be applied to minimize the spin orbitals. However, in order to

solve this energy expression, something must be known about the spin orbitals beforehand,

which is not the case. As such, an initial guess is made, and the spin orbital energies are then

iteratively minimized through basis sets.

Basis sets are sets of functions which are used to build the HF wave function. The

HF wave function is expressed as a Slater determinant formed from each individual

molecular orbital. Roothaan expressed the spin orbital in terms of a basis set.79

A contracted Gaussian function is essentially designed to reproduce a Slater

functional while minimizing computational costs. 76 Thus, a Slater S-type orbital, using the

aforementioned parameters to mimic real Slater functionals, with 𝑀 Gaussian functions, is

referred to an STO-MG basis set. An increased size of the contracted Gaussian results in a


34

better fit with a Slater functional. However, the increase comes at a severe computational

cost, and represents mainly the core orbitals which are generally not of relevance.

Consider the basis set, 6-311++G(d,p). This basis set is composed of 6 Gaussian

functions in each of the core orbitals, 3 tight functions, 1 intermediate function and 1 diffuse

function. The latter three functions are used to replicate the decay of the Slater-type basis

sets. In this particular case, additional diffuse functions are added to each heavy atom (+),

and diffuse functions are added to hydrogen (++). Finally, there is a set of d-type polarization

functions added to the heavy atoms (before the comma) and p-type polarization functions

added to the hydrogens (after the comma). The 6-311++G(d,p) basis set includes polarization

functions, diffuse functions and it is triple-zeta, so it is used in this work to provide

calculations for cluster model analysis. Other basis sets are possible, such as Dunning’s more

modern correlation consistent basis sets80, but these come at a higher computational expense.

These basis sets are named by their zeta-level, cc-pVXZ, where X is D (double-zeta), T

(triple-zeta), etc. The term “aug” may be added to add diffuse functions in a similar way to

the ++ notation.

Each spin orbital has an eigenvalue obtained using the Fock operator, 𝐟(𝐱𝑖). The

operator acts on the spin orbital wavefunction forming the Hartree-Fock equation,

𝐟(𝐱𝑖)𝜒𝑖(𝐱𝑖) = 휀𝑖𝜒𝑖(𝐱𝑖) 22

where the Fock operator is given by


35

𝑓(𝐱𝑖) = −∇𝑖

2

2− ∑

𝑍𝐴

𝑟𝑖𝐴

𝑀

𝐴=1

+ ∑[𝐽𝑏(𝐱𝑖) − 𝐾𝑏(𝐱𝑖)]

𝑁

𝑏=1

23

The sum of all of the spin orbital energies will therefore give an expression

representing the sum of all of the single electron kinetic energies, as well as the sum of all

the double electron Coulomb and exchange energies, from the 𝐽𝑏 and 𝐾𝑏 terms, respectively.

Thus, the HF energy for the system can be expressed as

𝐸𝐻𝐹 = −∇𝑖

2

2− ∑

𝑍𝐴

𝑟𝑖𝐴

𝑀

𝐴=1

+1

2∑∑[𝐽𝑏(𝐱𝑖) − 𝐾𝑏(𝐱𝑖)]

𝑁

𝑗=1

𝑁

𝑖=1

24

2.2.2 Møller-Plesset Perturbation Theory

Due to the single-Slater restriction of HF theory, the Hamiltonian does not give the

full description of the wavefunction representing the system in question. Møller-Plesset (MP)

perturbation theory81,82,83,84,85 is a post-HF method which introduces a significant amount of

improvement over HF by incorporating electron-correlation to the solution of the

wavefunction. It is a form of perturbation theory, meaning that it adds the correction to the

reference wavefunction by expressing the perturbation as the difference between the desired

true Hamiltonian and the reference Hamiltonian, which is the sum of the Fock operators

obtained by HF theory. The general case, the desired Hamiltonian is represented as the

original unperturbed HF Hamiltonian, 𝐻0, affected by a perturbation, 𝑉:


36

𝐻 = 𝐻0 + 𝜆𝑉 25

where 𝜆 is an ordering parameter.

The value of the perturbation is given by76:

𝑉 = ∑∑1

𝑟𝑖𝑗− ∑{∑[𝐽𝑏(xi) − 𝐾𝑏(x𝑖)]

𝑁

𝑏=1

}

𝑁

𝑖=1

𝑁

𝑗>𝑖

𝑁

𝑖=1

26

MP methods are usually named after the order by which the calculation is performed,

with MP2 and MP3 being calculations of second and third order correction to the energy.

Even higher order corrections can often be obtained, but are not commonly used due to the

costly nature of these calculations. MP1, representing first order perturbation theory, simply

regenerates the HF wavefunction, and consequently is not used.

MP2, the second-order correction to the wavefunction, is commonly used MP method

due to its relatively high degree of accuracy in representing the true Hamiltonian, at a

relatively low cost. The cost is reduced because this method uses the information obtained

during an HF calculation in the new calculation. Increasing the perturbation order to the

infinite degree, using an infinite basis set, will theoretically yield a perfect wavefunction

describing the molecular system in question.

2.2.3 Density Functional Theory

Density functional theory (DFT) is able to provide the ground state properties of most

systems and is one of the best methods for computing these properties. Instead of calculating


37

the energy using the orbital wavefunctions in the Schrödinger equation, DFT depends on the

electronic density of a system to determine its total energy. This approach was first proposed

by Hohenberg and Kohn86 later to be developed into the DFT method. 87 It has since become

one of the most popular, if not the leading method, for solving complex computational

problems involving large chemical systems.

As stated, DFT uses the electron density to solve the energy of the system, and not

the wavefunction. This was developed to avoid solving the orbital wavefunctions for every

electron, as is the case in HF theory. Since the electron density simply depends on three

dimensional coordinates, unlike HF theory, where each orbital has three spacial coordinates

as well as a spin coordinate, the computational challenge become much less cumbersome.

It was shown that the density functional could be used to solve the electronic energy

of a system. 86,87 The density function 𝜌(𝑟 ) is put into an energy functional, so as to obtain

an energy.

𝐸𝐷𝐹𝑇 = 𝐸[𝜌(𝑟 )] 27

In DFT, the density functional is not known, but various functionals are developed

and tested to give the best possible answers for various scenarios. The general form of the

functional is given as76:

𝐸[𝜌] = 𝑇𝑠[𝜌] + 𝐸𝑁𝑒[𝜌] + 𝐽[𝜌] + 𝐸𝑋𝐶[𝜌] 28

In the preceding expression, the energy functional depends on the terms incorporating

the kinetic energy, 𝑇𝑠[𝜌], the electron-nucleus attraction potential, 𝐸𝑁𝑒, the Coulombic


38

interaction between electrons, 𝐽, and the exchange-correlation, 𝐸𝑋𝐶. All of these functionals

are simply added together to obtain the total DFT energy.

In order to ensure the antisymmetry principle is obeyed, spin is introduced. 87 This is

found in the 𝑇𝑠 functional, where the electrons are assumed to be non-interacting. The

electronic density is obtained through this approach, but introduces some approximation to

DFT due to its reliance on HF theory.

The functional representing nuclear attraction is simply the interaction between the

nucleus and the electron density over all space. The Coulombic repulsion term is similar in

that it is the repulsion between two given electron charge distributions over a given area.

Finally, the exchange correlation term, 𝐸𝑋𝐶, accounts for the correction to the energy

due to the exchange energy (which is already treated in HF but not directly in DFT) as well

as the fact that there is indeed electron correlation that is not incorporated into the kinetic

energy term. The exchange-correlation functional is not known; it can, however, can be

guessed.

There are many different types of DFT, each one differing in its approach to the

exchange-correlation correction. The simplest is known as the Local Density Approximation

(LDA).76 In this approach, the charge felt by the electron density is assumed to be constant

over the space at which each point in the electronic density is probed, an unrealistic prospect.

An improvement over LDA, known as the Generalized Gradient Approximation88

(GGA) is used in this work. In this case, the exchange-correlation functional is dependent

on both the electron density and the derivative thereof, which gives the change of the electron


39

density over space. This class of functionals gives a better picture of the electron density over

space as it better reproduces the true state of the system.

The best attempt at approximating the exchange-correlation functions is through the

hybrid DFT approach. In short, hybrid DFT utilizes a bit of everything, so to speak. In fact,

this class of functionals incorporates both exchange from HF theory as well as correlation

from DFT, and other sources depending on the functional. One of the most popular

functionals is B3LYP.89,90 In this functional, the HF exact exchange is used, as well as the

LDA exchange and correlation. The GGA term is simply the LYP correlation functional. The

generalized expression is given as:

𝐸𝑋𝐶𝐵3 = (1 − 𝑎)𝐸𝑋

𝐿𝑆𝐷𝐴 + 𝑎𝐸𝑋𝐻𝐹 + 𝑏∆𝐸𝑋

𝐵88 + (1 − 𝑐)𝐸𝐶𝐿𝑆𝐷𝐴 + 𝑐∆𝐸𝑐

𝐺𝐺𝐴 29

where 𝑎, 𝑏, and 𝑐 are variable parameters.

DFT has difficulty modelling certain interactions. In general, DFT has difficulty

modelling long range interactions. 91 For example, radical-molecule interactions are prone to

error due to limited exchange modelling the charge transfer. 92 Similar issues arise with other

noncovalent interactions because DFT cannot properly model electron density over longer

distances, and so the exchange potential is represented by −0.2

𝑟, where the ideal case would

be seeing the exchange potential treated as −1

𝑟. 91,91 However, some hybrid DFT functionals

attempt to overcome these problems. These include BHandHLYP93, which uses a mixture of

both DFT and HF exchange energies and CAM-B3LYP94 (CAM = Couloumb attenuating

method), which introduces long range corrections in order to better treat noncovalent

interactions. PBE is a functional which has both exchange and correlation correction


40

incorporated. When this functional is corrected for long range, it is referred to as PBE, or

LC-PBE95,96,97 ( = 0.40 a.u.), depending on the corrections used. The M0598 and M0699

family of functionals are meta-GGA approaches to the exchange and correlation correction.

The preceding functionals have all been used in this thesis to evaluate the interaction

energies, as well as the NMR parameters of various simple compounds.

2.2.4 Computation of NMR Parameters using DFT

DFT is a useful computational method for calculating the magnetic properties of

atoms and molecules when they are under the influence of a magnetic field. In computing

properties such as magnetic shielding and spin-spin coupling, the chemist has the ability to

predict the outcome of NMR experiments. Additionally, DFT computational results may

provide complementary information to support the experimental findings of an NMR study.

When a molecule is subjected to an external magnetic field, the electrons are

perturbed in such a way that their properties are altered by the field. In DFT, the magnetic

properties of the electrons can be derived from the first and then second derivatives of the

total energy of the system with respect to two different perturbations, under the assumption

of a static magnetic field. In other words, all of the information needed to obtain magnetic

properties are within the wavefunction of the system.100

Nuclear shielding constants as well as indirect spin-spin coupling constants are

obtained from the derivative of the electronic energy of the system with respect to the

magnetic induction, and the nuclear magnetic moments to obtain the various contributions

to the J-coupling. 101 The second derivative is performed to determine further the magnetic


41

properties of the system. This is essentially derived from the electronic Hamiltonian for the

system, whereby the Hamiltonian is altered slightly for the dependence on the external

magnetic field.

DFT is, of course, an approximation method to solve the total energy of the system.

In doing so, it uses basis sets in order to represent molecular orbitals. When an infinite size

basis set is used, a perfect solution can be obtained. However, this is not possible, and

introduces the so-called “gauge origin problem” to the calculation of NMR parameters. It is

a problem that exists as a result of improper description of the magnetic field.102 This is

solved through the implementation of the gauge-invariant atomic orbitals (GIAO) method103,

being the default option in the Gaussian software.

2.2.5 Gauge Including Projector Augmented Wave DFT Calculations

Gauge Including Projector Augments Waves (GIPAW) DFT calculations 104 are

conducted on known crystal structures to obtain NMR parameters. GIPAW DFT is important

because it is able to account for the long-range effects of the crystal lattice on the NMR

properties, giving rise to more accurate results than in methods using single molecules.

GIPAW DFT is implemented in the CASTEP-NMR software code.105

Periodic boundary conditions are used to compute the total energy of a bulk

crystalline system. Since a crystalline material is made up of repeating unit cells, GIPAW

DFT is extremely useful for calculating NMR parameters of crystal structures in the solid

state. The main advantage of GIPAW DFT is that it is able to produce fairly accurate results


42

at a reasonable computational cost, whereas other traditional methods of DFT would not be

able to achieve similar results without astonishing computational cost.

In the GIPAW method, there are several factors that must be considered. First, a plane

wave basis set must be specified. Plane wave basis sets are used because of their improved

treatment of periodic systems. In addition, in order to minimize the number of nodes in the

core wavefunction due to the higher kinetic energy of the electrons, pseudopotentials provide

an alternative that replicates the core such that the computation can proceed better.106 Finally,

a cut-off energy is set in order to define the level of convergence for the calculation.

2.2.6 Counterpoise Correction

Counterpoise (CP) correction107 is used in computational chemistry in order to reduce

basis set superposition error (BSSE). When calculating bimolecular interactions, it is

important to consider the effect of BSSE because in the calculation of the complex, there

will be an artificial lowering of the overall energy because of the sharing of basis functions

between the nearby monomers.108 CP-correction provides a good way to correct for this error,

showing good results for noncovalent interactions at higher level calculations, such as

MP2.109

In the CP-correction program, the energy is calculated a number of times in Gaussian:

1. Dimer

2. Monomer 1 with dimer centred basis set (DCBS 1),

3. Monomer 2 with dimer centred basis set (DCBS 2)


43

4. Monomer 1 with monomer centred basis set (MCBS 1)

5. Monomer 2 with monomer centred basis set (MCBS 2)

The CP-corrected energy is thus given by a simple formulation of all of the calculated

energies110 (eqn. 30).

𝐸𝐶𝑃 = 𝐸𝑑𝑖𝑚𝑒𝑟 − 𝐸𝐷𝐶𝐵𝑆1 − 𝐸𝐷𝐶𝐵𝑆

2 30

The resulting energy value obtained from a calculation is the interaction energy (as a

function of intermolecular distances or angles). This is, however, different from binding

energy. In order to find the binding energy, the monomers are geometry optimized, then the

dimer is again geometry optimized at a fixed distance (2.825 A). The resulting energy is the

binding energy. The interaction energy is then the energy obtained when the geometries are

then frozen and the interaction distance is changed.

The NMR values are obtained from the output files from the dimer calculation. There

has been a study looking into the impact of BSSE on magnetic shielding constants. However,

for 13C and 15N, these corrections are normally on the order of 0.2 ppm for magnetic shielding

and 0.01 Hz for J-coupling (own data). As such, for the purpose of revealing NMR trends,

the CP-correction is not used to obtain corrected NMR parameters; only interaction energies.

2.3 Experimental Methodology of SSNMR

2.3.1 Experimental Setup

The NMR spectrometer (Figure 9) consists of several components which, when

acting together, allow the user to collect an NMR spectrum of a compound of interest,


44

whether it be in the liquid state or in the solid state. The major components of interest are the

magnet, the transmitter, the probe and the receiver.

The magnet provides the experiment with a strong, essentially homogenous magnetic

field in order to induce the Zeeman interaction, the fundamental process which gives rise to

the NMR transition. The energy corresponding to the NMR transition is dependent on the

strength of 𝐵0, so in the absence of a magnetic field, it would be difficult to observe an NMR

spectrum.

Figure 9. A 9.4 T NMR spectrometer magnet for the solid state. The superconducting coil is

found within the large cylindrical container, which also houses the cooling liquid.


45

2.3.2 Magic Angle Spinning

Magic angle spinning is a technique used in SSNMR which has the ability to reduce

or eliminate the anisotropies of certain NMR interactions such as dipolar coupling and

chemical shift anisotropy, which are orientationally dependent.111,112,113 MAS mimics the

isotopic tumbling of molecules in solutions through motional averaging. In solids, MAS can

reduce the anisotropies of chemical shift anisotropy, heteronuclear dipolar coupling

anisotropy and the J-coupling interaction anisotropy.111 Finally, the quadrupolar effect is

only partially averaged. In most cases, MAS has the average effect of sharpening the NMR

signals to yield liquid-like spectra. Its importance is very clear when it comes to the analysis

of complex spectra with many peaks at different chemical shifts. It is thus useful in chemical

shift assignment, or when changes in chemical shifts must be probed. However, due to the

reduction of the anisotropies, MAS has the effect of reducing the ease of observing some

anisotropic NMR parameters. Therefore, often times the NMR spectroscopist will also

perform static NMR experiments, where the sample remains motionless in the coil.

The need for MAS comes from the dependence of the angle of the PAS of certain

NMR interactions, such as magnetic shielding, with respect to 𝐵0 (eqn. 31). This dependence

is contained within a term in each of the respective Hamiltonian operators.

3 cos2 𝜃 − 1 31

𝜃 is the angle between the magnetic field and the z-axis of the interaction tensor.

Consequently, when 𝜃 = 54.74o, or the Magic Angle, the term is forced to zero. Thus, when

a sample is rotated around the magic angle axis, the averaging of the anisotropies occurs.


46

In order for the procedure to work, the spinning rate must be fast compared to the

anisotropy of the interaction, because there is a dependence of the cos 𝜃 term on the angular

velocity of the spinning rotor.114,115 As such, the faster the spinning speed, the more isotropic

the spectrum becomes. 59 A set of spinning side bands will be present, separated from the

isotropic peak by intervals of the spinning speed, in Hz. At the time of writing this thesis,

some of the fastest spinning rates of 111 kHz and 110 kHz that have been made commercially

available have been achieved by Bruker and JEOL, on their 0.7 mm116 and 0.75 mm117

CP/MAS probes, respectively.

2.3.3 Sensitivity Enhancement

2.3.3.1 Cross-Polarization

Cross-polarization (CP) is a technique used to improve the signals of spin-1

2 nuclei

which often have low natural abundance (n.a.) or are sparse within the sample (such as in the

case of 13C, n.a.= 1.1%) This technique is made possible due to the possibility for some

nuclei to transfer their polarization to other nuclei. In cases where the n.a. of the NMR active

nucleus is very low (< 1%), a CP experiment can drastically increase the signal-to-noise

ratio, and decrease the experimental time required in order to obtain decent results.

A CP experiment takes advantage of the fact hydrogen atoms possess an inherently

larger magnitude of polarization compared to other atoms of interest, such as 13C, 15N, and

31P, among others. This abundance in polarization is due to the protons’ gyromagnetic ratio,

, which is much larger than most other NMR active nuclei. The CP experiment will work

when the pulse applied to both the proton frequency channel and the frequency channel of


47

the nucleus of interest satisfies the Hartmann-Hahn matching condition118, meaning, the

nuclear precession frequencies become matched, thereby allowing a transfer of spin

polarization.

The Hartmann-Hahn matching condition can be demonstrated by first recalling that

E depends on the gyromagnetic ratio and the magnetic field. If two nuclear spins, 1H and

R, are coupled, and the application of an RF field induces local magnetic fields, then

ℎ𝑣 H1 = 𝛾 H1 𝛽1( H1 ) 32

ℎ𝑣𝑅 = 𝛾𝑅𝛽1(𝑅) 33

where 𝐵1 is the oscillating field generated by the respective nuclei. The Hartmann-Hahn

condition is fulfilled when:

𝛾 H1 𝐵1( H)1 = 𝛾𝐵𝐵1(𝑅) 34

so these two terms are matched by a common rf pulse.

A typical single pulse program using CP is shown in Figure 10. Following the 90o

pulse, a contact pulse is applied during which there is a transfer of polarization from the spin

A to spin B. Proton decoupling is applied during acquisition to ensure that maximum

sensitivity is gained on the nucleus of interest without interference from proton coupling.


48

Figure 10: Typical single pulse cross polarization pulse program. A 𝜋

2 pulse is applied to the

proton channel, followed by a 1H 13C contact time. This is followed by the acquisition

period coinciding with decoupling from the protons.

2.3.3.2 Data Acquisition Periods

A physical parameter that can be changed is the number of transients, or scans, that

are obtained in the experiment. The signal to noise ratio is very much dependent on this

number. As the number of transients increases, so does the signal-to-noise ratio.

Consequently, depending on the natural abundance of the nuclide being observed, it is typical

for an experiment to acquire hundreds, if not thousands of samplings to obtain a good end

signal. The signal intensity can be described as increasing as the square root of the number

of scans (eqn. 35).

𝑆

𝑁= √𝑛scans 35

Therefore, four times the number of scans is required to double the signal intensity

with respect to the background noise. However, the preceding expression shows that the


49

signal to noise ratio becomes limited as a function of time. As such, it is necessary to balance

the experimental time with the desired signal intensity.

Figure 11. The increase of the signal-to-noise ratio as a function of the number of time

dependent scans. Initially, the signal intensity grows rapidly, but as time continues to

increase, the interval at which the signal gain is achieved becomes impractically long.

2.4 Experimental Methods

2.4.1 Sample Preparation

Crystal structures exhibiting carbon tetrel bonds were selected from the CSD.

Conquest version 1.17 was used in conjunction with CSD version 5.36 with the November

2014 update, and the structures were visualized in Mercury version 3.5.1. The compounds

were chosen based on the criteria described in Chapter 3.

Salts containing tetrel bonds were investigated: sarcosinium tartrate, sarcosine

maleate and of N,N,N’,N’-tetramethylethylenediammonium succinate succinic acid.

0

20

40

60

80

100

120

140

160

180

200

0 10000 20000 30000 40000

Sig

na

l-to

-no

ise

Ra

tio

Number of Transients


50

Sarcosine was obtained from Sigma-Aldrich and used without further purification, and the

salts were collected according to the published procedures.44, 119,120

2.4.2 Powder X-ray Diffraction – Experimental Methods

The sample purity was confirmed by powder X-ray diffraction, using a Rigaku

Ultima IV X-ray diffractometer, with the Bragg-Brentano method with a monochromator

with CuK1 radiation ( = 1.54060 Å). Diffractograms were collected at room temperature

(298 ± 1 K) and with 2 values ranging from 2° to 5°, to 80° in increments of 0.02°.

Diffractograms were analyzed using the Rigaku PDXL 2 software and compared to existing

diffractograms in the PDF-2 2.1302 database and simulations generated using the Mercury

version 3.5.1 software provided from the Cambridge Crystallographic Data Centre (CCDC)

(CCDC entry numbers are 660888 and 159986, 142944 and 237950 for sarcosine,

sarcosinium tartrate, N,N,N’,N’-tetramethylethylenediammonium dichloride and of

N,N,N’,N’-tetramethylethylenediammonium succinate succinic acid, respectively).

2.4.3 Cluster Model Analysis

Computations on a library of model compounds were done several times, for

comparison, using B3LYP, MP2, BH&HLYP, CAM-B3LYP, LC-PBE, and LC-PBE-D3

(D3 refers to the addition of Grimme’s dispersion121) methods with the Gaussian 09

software122 on the Wooki cluster at the University of Ottawa. While the MP2 method cannot

calculate the NMR parameters, it is chosen as a method for comparing the energy calculated

by various DFT methods because it is able to properly treat noncovalent interactions.


51

In addition, a series of other functionals were also used to establish a cost benchmark

to identify the best functionals for calculating tetrel bonding energies (Table 2). The model

compounds were constructed and visualized via GaussView 4.1 software for Microsoft

Windows.123 All calculations were conducted with the 6-311++G(d,p) basis set. The tetrel

bond donor and acceptor moieties were each first geometry optimized using both density

functional theory (DFT) methods, or MP2. The DFT optimized precursors were combined

to form the tetrel-bonded systems that would be examined by various DFT methods, and the

MP2 optimized precursors were combined into models that would be analyzed via MP2. In

all cases the carbon tetrel bond length was set to 2.825 for geometry optimization. These

tetrel bonded models were then again geometry optimized by both DFT and MP2 methods

using counterpoise (CP) correction. Once optimized, the DFT and MP2 NMR parameters

were calculated. The GIAO method was used for magnetic shielding, specifying iop33(10=1)

in order to compute paramagnetic and diamagnetic contributions to the magnetic shielding

constants. Examples of Gaussian input files are in Appendix II – Sample of Computation

Input Files. EFGShield version 4.2 was used to extract the NMR parameters.124 Magnetic

shielding constants were then converted to chemical shift values with respect to the shielding

constant for tetramethylsilane (TMS), 184.1 ppm.125 Total J-coupling values were extracted

manually from the Gaussian output files calculated by DFT methods when the “spinspin”

keyword was specified. Taking into account basis set superposition error (BSSE), CP-

corrected interaction energies were obtained in units of kcal/mol and reported in this work.


52

2.4.4 Solid-State NMR

13C solid-state NMR was conducted at 9.4 T (𝜈𝐿(13C) = 100.613 MHz) under MAS

conditions (°) on an AVANCE III NMR spectrometer. Cross polarization

experiments (𝜈𝐿(1H) = 400.130 MHz) were performed with a spinning rate of 6 kHz in a

Bruker 4 mm HXY probe. Spectra were referenced externally to glycine at 176.4 ppm. In

each case, the contact time was 5000 s and the proton 90-degree pulse was 3.00 s. Several

thousand transients were typically acquired using a relaxation delay of 5 s.

Figure 12. A 4 mm MAS rotor compared to a Canadian Penny for scale. The cap of the rotor

is winged so that it may spin using a high pressure air stream. The spinning speed is adjusted

using an MAS controller fit onto the spectrometer console.

2.4.5 GIPAW DFT

GIPAW DFT calculations were carried out using the CASTEP-NMR software version

4.4126,105 on the Wooki cluster at the University of Ottawa. This was done in order to properly

treat the effects of the crystal lattice. Crystallographic information files were imported into

Materials Studio v. 4.4 (Accelrys) to generate input files. In all cases, the generalized gradient

approximation (GGA) with the functional of Perdew, Burke, and Ernzerhof (PBE)127 using

on-the-fly ultrasoft pseudopotentials128,129 was employed. Geometry optimization for the

hydrogen atoms, followed by NMR calculations on the sarcosine salts, were performed with


53

a 550.0 eV cutoff at the “fine” setting for the k-point grids. The calculation for sarcosine was

conducted using a 610.0 eV cutoff at the “ultra-fine” setting for the k-point grids. No

geometry optimization was performed for sarcosine. NMR parameters were extracted from

the CASTEP NMR output file using EFGShield version 4.2.124

Chapter 3 – Results and Discussion

54

Chapter 3 - Results and Discussion

3.1 Computational Investigations of NMR Trends in Tetrel Bonds

In this study, computational investigations were performed on a library of model

systems containing carbon tetrel bonds (Figure 14). It was previously demonstrated that

regions of negative charge energetically favour a weak interaction with the methyl carbon of

interest, especially when the methyl carbon is bonded to a strong electron-withdrawing

substituent.54 As discussed by Torres and DiLabio, DFT methods such as B3LYP often

cannot accurately describe medium to long range non-covalent interactions without some

sort of correction.91 Yet, the use of DFT is highly desirable because it can provide rapid and

accurate J-coupling values, an important NMR parameter providing structural information,

which can be used to probe the tetrel bond. A number of solutions have been offered to

overcome the shortfalls of DFT, including the use of dispersion correction,121 and the

packaging of improved exchange-correlation, as in the case of the M06 suite of functionals.91

In order to describe the tetrel bonding interaction energy, a study was performed to determine

a set of density functionals that could best represent the tetrel bond.

Model 6 (Figure 14) was chosen as the standard for this test. It was chosen due to its

relatively simple structure, and because it possesses a negative charge. The carbon tetrel bond

length was fixed at 2.825 Å, and the geometry was optimized by B3LYP/6-311++G(d,p)

with CP correction. The CP corrected bonding energy was obtained, using the 6-

311++G(d,p) basis set, for each of the functionals that were tested (Table 2). In each case,

the bonding energy was compared to the QCISD bonding energy, -2.72 kcal/mol.


55

Table 2. Functionals compared to QCISD in order to set a benchmark for determining the

highest performing functional as it applies to carbon tetrel bonding.

Density Functional

Correction

CP

corrected

energy

/ a.u.

CP

corrected

bonding

energy

/ kcal/mol

M06-2X D3 -285.03 -4.53

M06-2X - -285.03 -4.40

M06-HF130,131 - -285.05 -4.61

LC-ωPBE D3 -284.92 -4.74

LC-ωPBE - -284.98 -2.57

CAM-B3LYP D3 -284.98 -5.21

CAM-B3LYP - -285.05 -3.33

BHandHLYP - -284.99 -3.04

B3LYP D3 -285.10 -4.77

B3LYP - -285.17 -2.45

HF - -283.51 -1.83

CCSD132,133 - -284.42 -2.72

QCISD134 - -284.43 -2.72

A few functionals provide results within a relatively small difference of 0.5 kcal/mol

from the bonding energy obtained using QCISD (-2.72 kcal/mol), these being LC-PBE,

B3LYP, and BHandHLYP. CAM-B3LYP is also close but yielded an energy difference of

0.61 kcal/mol. Given the relative costs (Figure 13), the functionals that were chosen to

proceed representing a good mix of correlation and dispersion corrections that were chosen

for further calculations were B3LYP, BHandHLYP, CAM-B3LYP, LC-PBE and LC-

PBE-D3. We note that all of the M06 functionals took significantly longer and yielded

results which were further away in magnitude from the QCISD result.


56

Figure 13. Cost analysis of the various methods used in the test study on model 6. The red

hashed line represents the energy difference cut-off for this study at 0.5 kcal/mol, as

compared to the energy obtained in the QCISD calculation. All energies are at a tetrel bond

distance of 2.825 Å. The time taken for the QCISD calculation was 5,232 s.


57

Figure 14. Model compounds containing carbon tetrel bonds between methyl carbons and

oxygen-containing functional groups.

To explore trends in the NMR parameters, the LC-PBE, LC-ωPBE-D3,

BHandHLYP, B3LYP functionals, as well as the MP2 method, were used to perform


58

calculations of magnetic shielding tensors, on each of the compounds in the library (Figure

14), using the 6-311++G(d,p) basis set in Gaussian 09.122 Model structures were constructed

with carbon tetrel bond lengths increasing in 0.10 Å increments from 2.825 Å to 3.325 Å

(Figure 15), just over the sum of the vdW radii between carbon and oxygen, and carbon and

nitrogen, 3.22 Å and 3.25 Å, respectively.

Figure 15. A schematic showing how the tetrel bond lengths of the model compounds are

modified for the computations. The bond lengths are changed in 0.10 Å increments from

2.825 Å to 3.325 Å. The atomic coordinates are modified in the GaussView software.

The results for iso are presented graphically in Figure 16. At the time of this work,

in the vast majority of reported crystal structures, carbon tetrel bonds between methylamine

and oxygen have interaction lengths greater than 2.8 Å. However, there are a few cases where

the distance is shorter. The smallest value in the database is 2.591 Å,135 and the shortest

carbon tetrel bond between methylamine and a carboxylic acid is 2.825 Å.136

This analysis was done in order to expand the overall understanding of how the 13C

chemical shift of methyl group involved in a R-C···Y tetrel bond (R = C, F, N, N+1, S or S+1;

Y = O, O-1, or N) changes as a function of the interaction distance. The response of the

chemical shift to the tetrel bond angle was also assessed. The structures were constructed


59

with tetrel bond lengths of 2.925 Å, then varying the R-C···Y angle in increments of 5°

between 140° and 180°. This provides an adequate range over which to test chemical shift

response to the changing geometry of the tetrel bond and has been used previously as the

relevant range over which to search the CSD for existing tetrel bonded compounds.58


60

Figure 16. NMR computational investigations of model compounds. Calculated isotropic

chemical shifts of model compounds using (a) MP2, (b) B3LYP, (c) LC-PBE, (d) LC-

PBE-D3, (e) BHandHLYP, and (f) CAM-B3LYP are plotted against the reduced distance

parameter (rC∙∙∙Y) (top axis) and the interaction distance (d (C∙∙∙Y)) (bottom axis). Each plot

is fit by a quadratic polynomial function with R2 > 0.99 for all methods except CAM-B3LYP

(Table 12-Table 17). For spacing, data values for structures 8, 9, 13 and 14 are found in

Table 6 to Table 8 in Appendix I – Supplementary Data.

The model compounds are varied by the nature of their chemical structures and their

substituents, while the change in the C…Y tetrel bond distance remained consistent across all

of the examples (Figure 14). We also propose the use of the normalized distance parameter,


61

RX···Y, to measure the chemical shift response as well as the interaction energy as a function

of the interaction length (where the interaction distance is divided over the sum of the vdW

radii), as has been done for halogen bonds (eqn. 36).

𝑅X···Y =𝑑X···Y

∑𝑑VDW 36

Interestingly, in each case, the calculated 13C chemical shift increases quadratically

as the carbon tetrel bond length decreases, indicating of a correlation between the tetrel bond

strength and the chemical shift. This trend is not unexpected; it is reproduced experimentally

in 81Br halogen bonding, where the 81Br chemical shift increases significantly with the

shortening of the halogen bond distance, albeit with the possible competing effects of

hydrogen bonding.137 The polynomial function is stable beyond the vdW distance. The

computational data therefore suggest that, experimentally, the introduction of a carbon tetrel

bond should result in a positive 13C chemical shift on the order of up to 5 ppm. We note that

in the case of fluoro-substituted compounds (8 and 9), the computed chemical shift difference

is on the order of less than 1 ppm, albeit following the same trend. We note that while each

functional provides a different magnitude of chemical shift, they all show similar trends.

CP corrected interaction energies are reported in Figure 17. These computations

show that there is indeed a dependence of the interaction energy on the interaction distance.

Sometimes a local minimum is reached over the relevant range of distances, while sometimes

these minima reside closer or farther. However, there is no clear correlation with chemical

shift trends. Therefore, it can be expected that the presence of a tetrel bond, whether it is a


62

favourable or unfavourable interaction energetically, will provide the same chemical shift

trends as a function of distance.

A further analysis of the computed results (Figure 16) reveals that for the neutral

models (Figure 14), the chemical shift trend is largely dominated by changes in the

paramagnetic contribution, p, to the magnetic shielding constant, (Table 3). Conversely,

for the charged models, the changes in the diamagnetic contribution, d, are on the same

order of magnitude as the changes in the paramagnetic contribution. Also notable is that the

overall change in the magnitude of between B3LYP and LC-PBE is largely a result of

the change in the magnitude of the p values, reflecting the latter’s ability to better handle

longer range corrections. The paramagnetic contribution involves the mixing of virtual

orbitals with the ground electronic state (eqn. 37), while the diamagnetic contribution reflects

the structure of the ground electronic state (eqn. 38). A favourable overlapping of the ground

state orbitals (0) with the excited state orbitals (𝑛) results in paramagnetic deshielding. Given

that the overall changes to the chemical shift are very small relative to the total range of

known 13C chemical shifts, it is unproductive to attempt to further attribute the contributions

to specifics of the electronic structure of the tetrel bond.

𝜎𝑝𝛼𝛽

= −(𝜇0

4𝜋)(

𝑒2

2𝑚) ∑ {

⟨0|∑ 𝑟𝑘−3𝑙𝑘𝛼𝑘 |𝑛⟩⟨𝑛| ∑ 𝑙𝑘𝛽𝑘 |0⟩ + ⟨0|∑ 𝑙𝑘𝛽𝑘 |𝑛⟩⟨𝑛| ∑ 𝑟𝑘

−3𝑙𝑘𝛼𝑘 |0⟩

휀𝑛 − 휀01 }

𝑛≠0

37

𝜎𝑑𝛼𝛽

= (𝜇0

4𝜋)(

𝑒2

2𝑚) ⟨0|

𝑟2𝛿𝛼𝛽 − 𝑟ℎ𝛼𝑟ℎ𝛽

𝑟𝑘3 |0⟩ 38


63

where 𝜇0 is the mass of an electron, and 𝛿𝛼𝛽 is a Kroeneker delta, and the other terms are

previously defined.

Computed 13C chemical shift anisotropies (CSA, Haeberlen convention) for the

model compounds range from about 15 ppm for symmetric models (i.e., 1 and 2; (d = 3.325

Å)) to a high of almost 116 ppm for 14 (d = 2.825 Å) (Table 4). In all cases, the CSA

increases as the tetrel bond shortens.


64

Figure 17. Computed CP corrected interaction energy values vs. interaction distance of the

model compounds. Computed interaction energies using (a) MP2, (b) B3LYP, (c) LC-PBE,

(d) LC-PBE-D3, (e) BHandHLYP, and (f) CAM-B3LYP are plotted against the reduced

distance parameter (rC∙∙∙Y) (top axis) and the interaction distance (d(C∙∙∙Y)) (bottom axis). The

calculated interaction energies of the model compounds were obtained by 6-311G++(d,p)

with each respective functional. Each plot is fit by a quadratic polynomial function with R2

> 0.96 (Table 12 to Table 17 in Appendix I – Supplementary Data).


65

Table 3. Computed values of the diamagnetic and paramagnetic contributions to the

magnetic shielding constants (d, p, and t) for the model structures. Values were calculated

by B3LYP and LC-PBE using the 6-311++G(d,p) basis set.

B3LYP LC-PBE

Model

Structure

Interaction

Distance

/ Å d p t d p t

1 2.825 247.58 -79.22 168.37 247.81 -67.42 180.39

3.125 246.80 -75.34 171.47 246.71 -63.52 183.19

3.325 246.51 -73.85 172.66 246.25 -61.99 184.26

2 2.825 247.74 -79.39 168.34 246.76 -66.41 180.35

3.125 247.54 -76.10 171.44 246.59 -63.37 183.22

3.325 247.48 -74.79 172.69 246.57 -62.27 184.30

3 2.825 255.59 -110.45 145.14 257.13 -99.42 157.71

3.125 256.26 -109.89 146.37 257.69 -98.77 158.92

3.325 256.64 -109.73 146.92 258.06 -98.59 159.47

4 2.825 250.02 -103.79 146.23 251.24 -91.04 160.20

3.125 250.35 -101.54 148.81 251.20 -89.14 162.06

3.325 250.55 -100.73 149.81 251.25 -88.45 162.80

5 2.825 259.65 -114.58 145.07 262.58 -105.05 157.54

3.125 260.08 -113.92 146.16 263.34 -104.62 158.72

3.325 260.32 -113.63 146.69 263.80 -104.51 159.29

6 2.825 250.11 -104.92 145.19 251.03 -92.52 158.52

3.125 250.86 -103.60 147.26 251.76 -91.17 160.58

3.325 251.25 -103.04 148.21 252.21 -90.68 161.53

7 2.825 249.77 -112.55 137.22 250.88 -100.30 150.58

3.125 250.06 -110.15 139.91 251.02 -98.23 152.80

3.325 250.22 -109.27 140.95 251.16 -97.47 153.69

8 2.825 245.88 -198.11 47.78 248.08 -185.82 62.26

3.125 245.44 -197.46 47.98 247.18 -184.78 62.40

3.325 245.13 -197.04 48.09 246.68 -184.19 62.49

9 2.825 249.33 -182.74 66.59 249.39 -171.76 77.63

3.125 249.85 -182.97 66.88 249.83 -171.99 77.84

3.325 250.18 -183.17 67.01 250.15 -172.17 77.98

10 2.825 249.58 -113.75 135.83 251.28 -102.04 149.24

3.125 249.59 -110.56 139.04 251.06 -99.05 152.01

3.325 249.63 -109.25 140.38 251.00 -97.80 153.20

11 2.825 249.97 -86.20 163.77 250.47 -71.70 178.77

3.125 249.42 -82.79 166.64 249.92 -68.53 181.40

3.325 249.09 -81.24 167.84 249.52 -67.02 182.50


66

12 2.825 249.48 -92.30 157.18 251.46 -78.61 172.86

3.125 248.83 -90.89 157.94 250.67 -76.80 173.88

3.325 248.50 -90.14 158.36 250.21 -75.81 174.40

13 2.825 248.16 -143.09 105.07 249.13 -133.40 115.72

3.125 248.93 -142.52 106.41 249.76 -132.84 116.92

3.325 249.37 -142.40 106.97 250.15 -132.68 117.48

14 2.825 246.82 -141.52 105.30 247.78 -131.98 115.81

3.125 247.67 -141.32 106.35 248.49 -131.67 116.82

3.325 248.12 -141.22 106.89 248.87 -131.51 117.37

15 2.825 259.60 -122.14 137.46 261.51 -111.86 149.65

3.125 260.27 -121.50 138.77 262.05 -110.94 151.12

3.325 260.46 -121.03 139.44 262.21 -110.41 151.80

16 2.825 255.88 -118.03 137.85 257.54 -107.58 149.97

3.125 256.29 -117.11 139.18 257.81 -106.40 151.41

3.325 256.46 -116.64 139.82 257.94 -105.87 152.07


67

Table 4. Computed chemical shift anisotropy data for model compounds using stated functionals using the 6-311++g(d,p) basis set.

Model Structure

Functional

Interaction

Distance

/ Å 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

MP2

2.825 20.51 21.96 56.39 52.81 57.86 58.37 66.15 26.53 30.15 71.51 32.76 39.40 106.49 112.12 73.95 73.19

2.925 19.52 20.89 56.16 52.09 57.59 57.47 65.39 26.66 30.64 69.80 31.05 38.50 106.38 111.23 72.92 72.12

3.025 18.67 19.96 55.92 51.44 57.31 56.64 64.71 26.76 31.07 68.32 29.59 37.69 106.23 110.42 71.99 71.18

3.125 17.95 19.16 55.68 50.88 57.03 55.90 64.12 26.85 31.43 67.05 28.35 36.97 106.05 109.68 71.16 70.35

3.225 17.36 18.49 55.46 50.39 56.76 55.23 63.61 26.91 31.75 65.97 27.30 36.35 105.86 109.04 70.44 69.64

3.325 16.87 17.93 55.25 49.98 56.51 54.65 63.18 26.97 32.01 65.06 26.42 35.82 105.69 108.47 69.80 69.02

B3LYP

2.825 22.00 23.54 60.60 54.81 61.56 59.72 66.54 27.83 32.16 74.61 40.34 51.75 112.30 118.57 77.55 76.81

2.925 21.03 22.45 60.48 54.16 61.48 58.89 65.85 27.99 32.48 72.59 38.48 51.12 112.32 117.67 76.60 75.80

3.025 20.16 21.50 60.32 53.56 61.35 58.16 65.21 28.13 32.75 70.85 36.89 50.52 112.24 116.85 75.73 74.90

3.125 19.43 20.68 60.14 53.02 61.20 57.52 64.65 28.24 32.97 69.37 35.53 49.98 112.12 116.10 74.96 74.10

3.225 18.81 19.98 59.96 52.55 61.03 56.96 64.16 28.32 33.16 68.13 34.39 49.49 111.98 115.44 74.27 73.40

3.325 18.30 19.40 59.79 52.14 60.87 56.46 63.74 28.40 33.32 67.09 33.44 49.06 111.84 114.85 73.66 72.79

LC-PBE

2.825 18.32 19.89 56.12 50.89 57.72 56.71 61.96 31.25 34.34 67.89 31.81 43.04 109.89 115.91 73.48 72.67

2.925 17.38 18.83 55.92 50.06 57.46 55.69 61.26 31.48 34.66 66.21 30.16 42.20 109.85 115.01 72.38 71.54

3.025 16.57 17.92 55.70 49.35 57.18 54.77 60.63 31.66 34.93 64.76 28.76 41.43 109.74 114.18 71.39 70.55

3.125 15.89 17.14 55.47 48.72 56.90 53.94 60.08 31.79 35.14 63.53 27.58 40.76 109.59 113.43 70.53 69.68

3.225 15.33 16.49 55.25 48.19 56.63 53.21 59.60 31.89 35.32 62.48 26.58 40.17 109.43 112.77 69.77 68.93

3.325 14.87 15.95 55.06 47.76 56.37 52.57 59.21 31.97 35.47 61.62 25.75 39.65 109.28 112.20 69.11 68.29

LC-PBE-D3

2.825 18.32 19.89 56.12 50.89 57.72 56.71 61.96 31.25 34.34 67.89 31.81 43.04 109.89 115.91 73.48 72.67

2.925 17.38 18.83 55.92 50.06 57.46 55.69 61.26 31.48 34.66 66.21 30.16 42.20 109.85 115.01 72.38 71.54

3.025 16.57 17.92 55.70 49.35 57.18 54.77 60.63 31.66 34.93 64.76 28.76 41.43 109.74 114.18 71.39 70.55

3.125 15.89 17.14 55.47 48.72 56.90 53.94 60.08 31.79 35.14 63.53 27.58 40.76 109.59 113.43 70.53 69.68

3.225 15.33 16.49 55.25 48.19 56.63 53.21 59.60 31.89 35.32 62.48 26.58 40.17 109.43 112.77 69.77 68.93

3.325 14.87 15.95 55.06 47.76 56.37 52.57 59.21 31.97 35.47 61.62 25.75 39.65 109.28 112.20 69.11 68.29

CAM-B3LYP

2.825 21.15 22.73 59.44 53.84 60.23 58.74 65.75 28.66 32.13 73.63 37.61 47.52 112.33 118.67 77.01 76.22

2.925 20.13 21.60 59.25 53.13 60.08 57.86 65.02 28.84 32.45 71.62 35.70 46.68 112.30 117.73 75.93 75.10

3.025 19.24 20.60 59.03 52.48 59.90 57.08 64.34 28.98 32.72 69.88 34.05 45.92 112.18 116.86 74.96 74.09

3.125 18.48 19.75 58.81 51.90 59.70 56.39 63.74 29.09 32.94 68.41 32.66 45.23 112.02 116.08 74.09 73.21

3.225 17.84 19.03 58.60 51.39 59.50 55.78 63.22 29.18 33.13 67.16 31.48 44.62 111.85 115.38 73.32 72.45

3.325 17.31 18.42 58.40 50.96 59.31 55.25 62.79 29.25 33.30 66.12 30.50 44.09 111.69 114.77 72.64 71.78

BHandHLYP

2.825 20.14 21.65 56.79 51.09 57.91 55.98 62.78 25.33 29.25 69.93 37.32 46.54 105.24 111.02 73.12 72.35

2.925 19.10 20.50 56.51 50.34 57.64 55.06 62.00 25.49 29.55 67.98 35.25 45.67 105.10 110.06 72.05 71.23

3.025 18.19 19.50 56.23 49.67 57.37 54.25 61.30 25.61 29.82 66.32 33.49 44.88 104.91 109.18 71.09 70.25

3.125 17.43 18.65 55.97 49.09 57.09 53.54 60.70 25.71 30.04 64.91 32.02 44.18 104.70 108.40 70.24 69.40

3.225 16.80 17.94 55.72 48.59 56.84 52.91 60.18 25.79 30.23 63.72 30.78 43.57 104.49 107.71 69.49 68.66

3.325 16.29 17.35 55.50 48.17 56.60 52.36 59.75 25.85 30.39 62.74 29.76 43.04 104.30 107.12 68.85 68.02


68

A change in the chemical shift as a function of the interaction angle was also

observed. The change in angle yielded only small changes, on the order of less than 2 ppm

between 140° and 180°. Overall, as the angle gets closer to 180°, the chemical shift decreases.

The largest magnitude of change occurs between 140° and 160°, which could be explained

by the gradual approach of Y to the methyl hydrogens, introducing a C-H∙∙∙Y hydrogen bond,

and begins to slow down as the angle approaches 180° as the tetrel bond becomes dominant.

It is clear then that the tetrel bond distance remains the dominant effect on the carbon

chemical shift and consequently, any effect of the angle on the chemical shift is expected to

be negligible or overshadowed by other effects.

In additional to chemical shifts and energy, J-couplings are valuable parameters for

the characterization of noncovalent interactions. Trans-hydrogen bond J-coupling has been

studied extensively as an important tool for obtaining direct experimental evidence of

hydrogen bonding via NMR.138,139,140,141,142,143,144 Recently, computed J-coupling constants

have been reported for a series of noncovalent interactions, including pnicogen bonding,

chalcogen bonding and halogen bonding.145,146,43 For instance, in a recent study by Del Bene

et al., the interaction distance in a P-P pnicogen bond is estimated by the calculated

correlation between the J-coupling and the interaction distance.146 As such, J-coupling could

provide a valuable probe of tetrel bonds.

In the present study, J-coupling was calculated for each of the model compounds

(Figure 14) using the LC-PBE-D3, BHandHLYP, and CAM-B3LYP functionals. Total

1cJ(13C,17O/15N) coupling constants across the carbon tetrel bond are plotted in Figure 18 as

a function of the interaction distance in order to gain information as to whether the J-coupling


69

can provide evidence for the presence of the carbon tetrel bond. Here, we propose use of the

“1cJ” nomenclature to denote trans-carbon bond coupling, in analogy with the “1hJ, 2hJ” etc.

labels used in the literature for trans-hydrogen bond couplings. In each case, the roles of the

Fermi contact (FC), spin-dipolar (SD), paramagnetic spin-orbital (PSO), and diamagnetic

spin-orbital (DSO) mechanisms were assessed to evaluate their contributions to the total J-

coupling (Table 6 to Table 8, Appendix I – Supplementary Data). In all of the model

structures, the FC mechanism contributes 100% ± 5% of the total, suggesting an overlap of

orbitals with spin density centered at the nuclei of the carbon and the oxygen or nitrogen

atoms. The importance of various coupling mechanisms in different models suggests a

delicate interplay between these mechanisms147 depending on the exact geometrical details

and charge state of the model.

It can be observed in all cases that the coupling value (1cJ(13C,17O) or 1cJ(13C,15N))

becomes more negative as the interaction distance becomes shorter. Clearly there exists a

correlation between interaction distance and the magnitude of 1cJ, thereby providing a new

parameter for the study of carbon tetrel bonds. In each case, a second-order polynomial fits

the data with a correlation coefficient, R2, of at least 0.99 (Table 9-Table 11, Appendix I).

The data corroborate the findings for pnicogen and halogen bonding as well, where

analogous correlations have also been observed computationally. In one case of pnicogen

bonding, J(31P,31P) decreases from hundreds of hertz toward zero as the interaction distance

is increased. 146 In the case of J-coupling across Cl···N halogen bonds, computations show

that the J(35/37Cl,15N) value approaches 0 Hz from values of between approximately -60 and

-90 Hz, as the interaction distance is increased. 70


70

Figure 18. Computed J-coupling for model compounds. Graphs represent 1cJ-coupling

values between 13C and either 17O or 15N using (a) The LC-PBE-D3, (b) BHandHLYP, and

(c) CAM-B3LYP methods. In each case, the 6-311++G(d,p) basis set is used. Each plot is fit

by a quadratic polynomial function with R2 > 0.99 (Table 9 to Table 11 in Appendix I –

Supplementary Data).

3.2 Experimental NMR Investigations of Noncovalent Tetrel Bonds

The calculations on isolated model systems provide valuable insight into the

relationship between NMR parameters and tetrel bonds. Given that the crystal lattice can

influence NMR parameters, a further step was taken in order to investigate dependence of

carbon chemical shift on the carbon tetrel bond in the case of crystal structures. The CSD

was used to search for published crystal structures that contain carbon tetrel bonds. Because

there is not yet a universally accepted definition of a tetrel bond, candidate compounds were

screened for using two criteria, which are in accordance with the IUPAC standard for halogen

bonds: (1) The C···Y interaction distance must be within the sum of their van der Waals radii

and (2) R-C···Y angle must be within 160° and 180°.148 We note that these criteria are


71

slightly stricter than those used in the work of Thomas and co-workers, wherein the angle

range used is 140° to 180°.58 Among a large number of hits were sarcosinium tartrate (dC...O

= 3.08 Å) (Figure 6), sarcosine maleate (dC...O = 2.96 Å), and N,N,N’,N’-

tetramethylethylenediammonium succinate succinic acid (dC...O = 3.07 Å) (Figure 19) which

were found to be good carbon tetrel-bonding candidates for this study.44,149 Each salt is

compared to its corresponding salt lacking a tetrel bond.

Figure 19. The tetrel bond present in N,N,N’,N’-tetramethylethylenediammonium succinate

succinic acid. The interaction distance is 3.07 Å.

Although the tetrel bonds in these compounds are significant on the basis of the C…O

distances, there was concern with respect to the possible impact of competing weak C-H…O

hydrogen bonds. In the case of sarcosinium tartrate, the distances between O and H are

greater than 2.72 Å, the sum of their vdW radii. In sarcosinium maleate, there is a single

hydrogen 2.70 Å from the oxygen, according to the published crystal structure. Thus, for


72

these two salts, the strengths of the tetrel bonds, as judged by the reduced distance parameter

(RX···Y; eqn. 36) are significant whereas the strength of hydrogen bonds as quantified by the

same criteria is far less important. Generally, the methyl protons are splayed with respect to

the oxygen. The possible role of trifurcated hydrogen bonds in such systems has been

discussed in ref 58. In the case of N,N,N’,N’-tetramethylethylenediammonium succinate

succinic acid, there are not competing hydrogen bonds directly with the tetrel bonded oxygen

atom, however, the methyl hydrogens still make close contacts with other oxygen atoms in

the system. Regardless of the possible weak influence of a weak trifurcated hydrogen bond,

the presence of a tetrel bond means that de facto this interaction contributes to the observed

chemical shift.

The compounds were first made according to the literature sources (See section 2.4.1).

PXRD was used to confirm the identities of the substances. The PXRD show good agreement

between the obtained compounds and the simulated source. In the case of sarcosine, there is

only an extra peak at about 26o, but one peak missing at about 33o on the 2𝜃 axis (Figure

20), while sarcosinium tartrate shows almost perfect agreement with the simulated

diffraction patters, albeit with stronger signal intensities (Figure 21). The N,N,N’,N’-

tetramethylethylenediammonium salts are shown to have good agreement with their

simulated diffraction patterns (Figure 22 and Figure 23).


73

Figure 20. Powder X-Ray diffractogram of sarcosine. The simulated diffractogram (a) was

obtained using the Mercury version 3.5.1 software provided by the CCDC. The experimental

diffractogram (b) was obtained from a powdered sample using a Rigaku Ultima IV X-ray

diffractometer.


74

Figure 21. Powder X-Ray diffractogram of sarcosinium tartrate. The simulated

diffractogram (a) was obtained using the Mercury version 3.5.1 software provided by the

CCDC. The experimental diffractogram (b) was obtained from a powdered sample using a

Rigaku Ultima IV X-ray diffractometer.


75


dichloride. The simulated diffractogram (a) was obtained using the Mercury version 3.5.1

software provided by the CCDC. The experimental diffractogram (b) was obtained from a

powdered sample using a Rigaku Ultima IV X-ray diffractometer.

a

b


76


succinate succinic acid. The simulated diffractogram (a) was obtained using the Mercury

version 3.5.1 software provided by the CCDC. The experimental diffractogram (b) was

obtained from a powdered sample using a Rigaku Ultima IV X-ray diffractometer.

The GIPAW DFT computed and experimental 13C solid state NMR chemical shifts

corresponding the sarcosine and N,N,N’,N’-tetramethylethylenediammonium methyl groups

a

b


77

(Figure 24 to Figure 27) involved in the both in the presence of a carbon tetrel bond and in

the absence are reported in Table 5. In the same table, the C…O noncovalent bond distances,

as well as the N-C covalent bond distances are obtained from the CSD.

Figure 24. 13C CP/MAS spectra of sarcosine (top) and sarcosinium tartrate (bottom).

Spinning sidebands are denoted with asterisks. 𝐵0 = 9.4 T.


78


(CP/MAS) NMR spectra of the methyl carbon associated with a tetrel bond. 𝐵0 = 9.4 T. (a)

Sarcosinium Tartrate. (b) Sarcosine.


79

Figure 26. 13C CP/MAS spectra of N,N,N’,N’-tetramethylethylenediammonium dichloride

(top) and N,N,N’,N’-tetramethylethylenediammonium succinate succinic acid (bottom).

Spinning sidebands are denoted with asterisks. 𝐵0 = 9.4 T.


80


(CP/MAS) NMR spectra of the methyl carbon associated with a tetrel bond. 𝐵0 = 9.4 T. (a)

N,N,N’,N’-tetramethylethylenediammonium dichloride. (b) N,N,N’,N’-

tetramethylethylenediammonium succinate succinic acid.


81

Table 5. Calculated GIPAW and experimental 13C isotropic chemical shifts for the methyl

carbon on sarcosine compounds.

compound

N-C

Bond

Length

/ Å

Interaction

Distance

(C…O)

/ Å

RC∙∙∙O

iso(13C)

calc.

/ ppm

calc.

/ppm

calc.

iso(13C)

exp.

/ ppm

Sarcosine 1.4813(3) n/a n/a 37.9 56.8 0.773 31.5

Sarcosinium Tartrate 1.485(3) 3.08 0.96 43.6 61.8 0.604 34.7

Sarcosinium Maleate 149 1.497(2) 2.96 0.92 47.9 55.0 0.753 36

TMEDAa HCl 1.487(4) n/a n/a 27.8 72.1 0.879 41.4

1.486(4) n/a n/a 32.0 86.8 0.635 46.0

TMEDAa succinate 1.493(2) 3.07 0.95 33.4 89.6 0.646 44.3

1.487(2) 3.26 1.01 31.4 73.3 0.898 46.2

(a) TMEDA refers to N,N,N’,N’-tetramethylethylenediammonium.

(b) Entries in bold correspond to the methyl carbons of interest. In TMEDA succinate, the bolded

entry participates in the -hole interaction, whereas the other methyl carbon does not.

It is interesting to note that in each of the cases where the carbon tetrel bond is present,

the introduction of this interaction causes the chemical shift of the methyl group to increase.

In addition, the N-C bond lengthens in the presence of the tetrel bond. These trends are

reflected in both the GIPAW calculations and the experimental results where the chemical

shift increases are on the order of 5 to 10 ppm and 3 to 5 ppm, respectively. The magnitudes

of the increases noted from solid-state NMR spectroscopy experiments mirror much more

closely the increases calculated for isolated model systems.

The trends predicted by the GIPAW calculations are nevertheless also consistent with

the experimental data. Note that a comparison of the experimental and calculated absolute

values of the chemical shifts, while perhaps providing some insight into the overall accuracy


82

of the computational method and absolute shielding scale used, does not detract from the

findings as far as the trend in the values as a function of the tetrel bond distance.

We note that in the cases of the sarcosine salts, the amine becomes protonated,

whereas sarcosine itself is neutral. We assessed the potential competing effect of this

protonation on the methylamine 13C chemical shift and found there to be a slight difference

between the neutral and charged molecules. In a literature review, it was noted that the effect

of protonation of sarcosine causes a decrease in the methylamine 13C chemical shift by 1.83

ppm, from 35.75 ppm to 33.92 ppm (in solution where the carboxylate is negatively charged).

150 This trend was confirmed by Batchelor and co-workers, who noted that the 13C

protonation shift of a methylamine is -2.04 ppm 151, while Thursfield and coworkers

distinguish a chemical shift difference of about -2.7 ppm between monomethylamine (=

26.9 to 27.5 ppm) and the corresponding cation (= 24.3 to 24.8 ppm) during a conversion

of methanol and ammonia over the zeolite H-SAPO-34. 152 Thursfield’s results are also

confirmed by Jiang et al. 153 Given these experimental results reported in the literature,

protonation of the amine in sarcosine would therefore be expected to produce a small

negative change in the chemical shift, on the order of 2 to 3 ppm. However, our experimental

and computational data present a change in chemical shift in the opposite direction upon the

combined introduction of a tetrel bond and amine protonation. Therefore, this strongly

suggests that the dominant cause for this change is the introduction of the carbon tetrel bond.

Chapter 4 – Conclusions

83

Chapter 4 - Conclusions

This combined computational and experimental work has provided several outcomes

and insights into the nature of tetrel bonding. First, the quantum chemical calculations on

isolated model systems show that the chemical shifts of carbon atoms acting as tetrel bond

donors increase with the strength of the interaction. Both diamagnetic and paramagnetic

contributions to the magnetic shielding constant are responsible for this trend. Furthermore,

13C chemical shift anisotropies increase with the strength of the interaction.

In agreement with the computations on isolated models, calculations using periodic

boundary conditions to model the effects of an infinite crystal lattice (GIPAW DFT) show

that the chemical shifts of carbon atoms acting as tetrel bond donors increase relative to

parent compounds where tetrel bonds are absent. Experimental data for sarcosine, where no

tetrel bond is present, and for two sarcosine salts exhibiting tetrel bonds in the solid state

confirm the computational trends described by both the cluster model analysis as well as the

GIPAW DFT calculations on published crystal structures.

Cluster model calculations of trans-tetrel bond J couplings show that the magnitude

of 1cJ(13C,17O) increases from zero to several hertz as the C…O interaction distance is

decreased to less than the sum of their van der Waals radii. The couplings are typically, but

not always, entirely due to the Fermi-contact coupling mechanism.

In summary, the present work provides compelling computational and experimental

evidence that the carbon tetrel bond has an influence on NMR parameters in the solid state,

thus creating opportunities to use NMR crystallography to characterize tetrel-bonded

supramolecular architectures and functional materials.

Chapter 4 – Conclusions

84

There is still work to be done in completing the characterization of the carbon tetrel

bond. Concurrently, there is an opportunity for further study of other tetrel elements in order

to understand the nature of the electronic structures of these bonds. Further research

involving silicon, germanium, tin, and lead would be useful using both SSNMR methods and

ab initio computational studies using our state-of-the-art equipment at the National

Ultrahigh-Field NMR Facility for Solids. The crystal structures will first be solved by X-ray

diffraction, and the study of these nuclides by multinuclear SSNMR will provide key data

relevant to this project. The chemical shift response as a result of the formation of the tetrel

bond, as well as other NMR parameters, will assist in developing a clear picture of the tetrel

bond. Quantum calculations using density functional theory at the Canadian High

Performance Computing Virtual Laboratory will be used to complement the experimental

data and confirm any observations.

85

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Appendix I – Supplementary Data

103


Table 6. Raw data obtained from calculations (BHandHLYP/6-311++G(d,p)) of

1cJ(13C,17O/15N) in model structures. All values are reported in Hz.

Model

Structure

Interaction Distance

/Å FC SD PSO DSO Total J %FC

1

2.825 -5.7774400 -0.0033046 0.2211940 -0.0384239 -5.5979800 103.21

2.925 -4.4712100 -0.0046878 0.1923000 -0.0361786 -4.3197800 103.51

3.025 -3.4094900 -0.0053476 0.1677860 -0.0341417 -3.2811900 103.91

3.125 -2.6226900 -0.0055014 0.1470290 -0.0322869 -2.5134500 104.35

3.225 -1.9885400 -0.0053855 0.1294620 -0.0305911 -1.8950500 104.93

3.325 -1.4673700 -0.0051835 0.1145940 -0.0290354 -1.3870000 105.79

2

2.825 -5.9705500 -0.0078246 0.1891870 -0.0452860 -5.8344800 102.33

2.925 -4.6327300 -0.0069752 0.1657100 -0.0427530 -4.5167500 102.57

3.025 -3.5428000 -0.0061207 0.1452890 -0.0404468 -3.4440800 102.87

3.125 -2.7252700 -0.0052762 0.1276690 -0.0383392 -2.6412200 103.18

3.225 -2.0759500 -0.0045096 0.1125460 -0.0364059 -2.0043200 103.57

3.325 -1.5376900 -0.0039040 0.0996200 -0.0346266 -1.4766000 104.14

3

2.825 -8.4040300 -0.0281782 0.1026520 -0.0426263 -8.3721800 100.38

2.925 -6.5924800 -0.0231170 0.0990098 -0.0401181 -6.5567000 100.55

3.025 -5.1447500 -0.0190264 0.0943790 -0.0378430 -5.1072400 100.73

3.125 -3.9759900 -0.0157842 0.0892440 -0.0357710 -3.9383000 100.96

3.225 -3.0596900 -0.0131830 0.0839403 -0.0338769 -3.0228100 101.22

3.325 -2.3299300 -0.0111324 0.0786916 -0.0321394 -2.2945100 101.54

4

2.825 -6.8198200 -0.0044630 0.1741670 -0.0416687 -6.6917800 101.91

2.925 -5.3073500 -0.0047536 0.1525780 -0.0392216 -5.1987400 102.09

3.025 -4.0825800 -0.0046334 0.1342270 -0.0370014 -3.9899800 102.32

3.125 -3.1550400 -0.0042736 0.1186300 -0.0349796 -3.0756700 102.58

3.225 -2.4098300 -0.0037883 0.1053690 -0.0331312 -2.3413800 102.92

3.325 -1.7981900 -0.0033615 0.0940816 -0.0314359 -1.7389100 103.41

5

2.825 -9.8252900 -0.0168635 0.0579256 -0.0483889 -9.8326100 99.93

2.925 -7.7046100 -0.0132438 0.0628782 -0.0457005 -7.7006800 100.05

3.025 -6.0094900 -0.0105396 0.0647445 -0.0432492 -5.9985400 100.18

3.125 -4.6638700 -0.0085171 0.0645585 -0.0410055 -4.6488400 100.32

3.225 -3.5875200 -0.0070535 0.0630627 -0.0389446 -3.5704500 100.48

3.325 -2.7701800 -0.0058979 0.0607799 -0.0370452 -2.7523400 100.65

6

2.825 -9.9455000 -0.0232848 0.0420864 -0.0432029 -9.9699000 99.76

2.925 -7.8446900 -0.0165779 0.0470122 -0.0407596 -7.8550200 99.87

3.025 -6.1444700 -0.0115388 0.0484756 -0.0385370 -6.1460700 99.97


104

3.125 -4.7858100 -0.0077824 0.0477239 -0.0365071 -4.7823800 100.07

3.225 -3.7199100 -0.0050022 0.0456410 -0.0346461 -3.7139200 100.16

3.325 -2.8793500 -0.0029973 0.0428363 -0.0329341 -2.8724500 100.24

7

2.825 -6.6463000 -0.0044124 0.1966320 -0.0454815 -6.4995600 102.26

2.925 -5.1631800 -0.0053627 0.1717160 -0.0428884 -5.0397200 102.45

3.025 -3.9694600 -0.0056746 0.1507090 -0.0405297 -3.8649600 102.70

3.125 -3.0572400 -0.0055989 0.1329750 -0.0383764 -2.9682400 103.00

3.225 -2.3201700 -0.0053059 0.1179810 -0.0364033 -2.2439000 103.40

3.325 -1.7354800 -0.0049659 0.1052800 -0.0345894 -1.6697600 103.94

8

2.825 -0.1271800 0.0361270 0.0242229 -0.0618174 -0.1286480 98.86

2.925 -0.0054982 0.0319578 0.0221303 -0.0566491 -0.0080593 68.22

3.025 0.0631498 0.0283092 0.0202108 -0.0520746 0.0595952 105.96

3.125 0.1003810 0.0251565 0.0185288 -0.0480110 0.0960552 104.50

3.225 0.1167330 0.0224498 0.0170902 -0.0443888 0.1118850 104.33

3.325 0.1160610 0.0201338 0.0158772 -0.0411491 0.1109230 104.63

9

2.825 -4.2597800 0.0225266 -0.0167204 -0.0587748 -4.3127500 98.77

2.925 -3.3080100 0.0235869 -0.0086157 -0.0546399 -3.3476700 98.82

3.025 -2.5653100 0.0236232 -0.0031007 -0.0509301 -2.5957100 98.83

3.125 -1.9577100 0.0229638 0.0006016 0.0006016 -1.9817400 98.79

3.225 -1.4938800 0.0219128 0.0030470 -0.0445719 -1.5135000 98.70

3.325 -1.1350300 0.0206610 0.0046335 -0.0418364 -1.1515700 98.56

10

2.825 -6.0983126 0.0017227 0.0050878 -0.0329137 -6.1244174 99.57

2.925 -4.9026536 0.0013808 0.0072425 -0.0310196 -4.9250411 99.55

3.025 -3.9133502 0.0011910 0.0082917 -0.0292960 -3.9331708 99.50

3.125 -3.1038207 0.0010870 0.0086249 -0.0277219 -3.1218317 99.42

3.225 -2.4422932 0.0010361 0.0085185 -0.0262793 -2.4590137 99.32

3.325 -1.9123558 0.0010064 0.0081643 -0.0249530 -1.9281365 99.18

11

2.825 -7.2071145 -0.0094666 0.0007135 -0.0331168 -7.2489860 99.42

2.925 -5.7420051 -0.0097103 0.0041096 -0.0313214 -5.7789250 99.36

3.025 -4.5406510 -0.0095844 0.0060870 -0.0296808 -4.5738396 99.27

3.125 -3.5653329 -0.0346615 0.0071027 -0.0281762 -3.5956599 99.16

3.225 -2.7938314 -0.0087708 0.0074845 -0.0267919 -2.8219140 99.00

3.325 -2.1646509 -0.0082427 0.0074672 -0.0255144 -2.1909380 98.80

12

2.825 -10.0660045 -0.0078429 -0.0085749 -0.0343485 -10.1167693 99.50

2.925 -8.1384291 -0.0081146 -0.0036897 -0.0324641 -8.1826852 99.46

3.025 -6.5352910 -0.0081154 -0.0003020 -0.0307434 -6.5744412 99.40

3.125 -5.2075650 -0.0079637 0.0019808 -0.0291667 -5.2427174 99.33

3.225 -4.1433839 -0.0076689 0.0034615 -0.0277172 -4.1753100 99.24

3.325 -3.2698338 -0.0073289 0.0043746 -0.0263804 -3.2991789 99.11

13

2.825 -8.1897100 -0.0169981 0.1368380 -0.0484516 -8.1183300 100.88

2.925 -6.3826800 -0.0157425 0.1239260 -0.0456354 -6.3201300 100.99

3.025 -4.9396400 -4.9396400 0.1126660 -0.0430766 -4.8843300 101.13


105

3.125 -3.8350900 -0.0127527 0.1027790 -0.0407428 -3.7858100 101.30

3.225 -2.9168100 -0.0113448 0.0940566 -0.0386065 -2.8727000 101.54

3.325 -2.1867600 -0.0101220 0.0863351 -0.0366446 -2.1471900 101.84

14

2.825 -8.5663459 -0.0077326 0.0062075 -0.0357135 -8.6035743 99.57

2.925 -6.9161603 -0.0089168 0.0062827 -0.0337083 -6.9525050 99.48

3.025 -5.5426070 -0.0094103 0.0062205 -0.0318789 -5.5776753 99.37

3.125 -4.3996486 -0.0094761 0.0060534 -0.0302040 -4.4332861 99.24

3.225 -3.4964308 -0.0092233 0.0058142 -0.0286656 -3.5285112 99.09

3.325 -2.7531803 -0.0088270 0.0055360 -0.0272486 -2.7837317 98.90

15

2.825 -9.3865782 -0.0086330 0.0116579 -0.0359643 -9.4195283 99.65

2.925 -7.6781092 -0.0087286 0.0128835 -0.0339973 -7.7079593 99.61

3.025 -6.2383752 -0.0085638 0.0133839 -0.0322006 -6.2657564 99.56

3.125 -5.0195290 -0.0082747 0.0133938 -0.0305540 -5.0449605 99.50

3.225 -4.0311234 -0.0078702 0.0130872 -0.0290397 -4.0549417 99.41

3.325 -3.2214115 -0.0074234 0.0125935 -0.0276429 -3.2438833 99.31

16

2.825 -8.8206187 -0.0098034 0.0101711 -0.0340361 -8.8542983 99.62

2.925 -7.1904781 -0.0100231 0.0109761 -0.0321483 -7.2216749 99.57

3.025 -5.8218064 -0.0098948 0.0112125 -0.0304252 -5.8509131 99.50

3.125 -4.6605283 -0.0095923 0.0110726 -0.0288471 -4.6878956 99.42

3.225 -3.7354560 -0.0091251 0.0106975 -0.0273967 -3.7612802 99.31

3.325 -2.9739700 -0.0086028 0.0101924 -0.0260599 -2.9984336 99.18


106

Table 7. Raw data obtained from calculations (LC-PBE-D3/6-311++G(d,p)) of


Model

Structure



1

2.825 -5.7930600 0.0005746 0.2305720 -0.0378695 -5.5997800 103.45

2.925 -4.4339900 -0.0015727 0.1988320 -0.0356548 -4.2723800 103.78

3.025 -3.3752800 -0.0027946 0.1723260 -0.0336477 -3.2393900 104.19

3.125 -2.5495100 -0.0034511 0.1501720 -0.0318206 -2.4346100 104.72

3.225 -1.9178000 -0.0037408 0.1316800 -0.0301513 -1.8200100 105.37

3.325 -1.4341400 -0.0038239 0.1162390 -0.0286203 -1.3503400 106.21

2

2.825 -6.0089700 -0.0039513 0.1973090 -0.0446880 -5.8603000 102.54

2.925 -4.6076600 -0.0041334 0.1710760 -0.0421888 -4.4829000 102.78

3.025 -3.5145100 -0.0040177 0.1487570 -0.0399152 -3.4096900 103.07

3.125 -2.6592700 -0.0037775 0.1298370 -0.0378379 -2.5710500 103.43

3.225 -2.0049800 -0.0034803 0.1138820 -0.0359334 -1.9305100 103.86

3.325 -1.5022400 -0.0031926 0.1004780 -0.0341809 -1.4391400 104.38

3

2.825 -8.0576200 -0.0185941 0.1264120 -0.0420964 -7.9918900 100.82

2.925 -6.2217000 -0.0154347 0.1174050 -0.0396212 -6.1593500 101.01

3.025 -4.7801800 -0.0128509 0.1086360 -0.0373767 -4.7217700 101.24

3.125 -3.6555100 -0.0107681 0.1003280 -0.0353333 -3.6012800 101.51

3.225 -2.7776700 -0.0091113 0.0926012 -0.0334664 -2.7276500 101.83

3.325 -2.0962600 -0.0077884 0.0855118 -0.0317541 -2.0503000 102.24

4

2.825 -5.7844300 0.0047817 0.0188364 -0.0397117 -5.8005200 99.72

2.925 -4.4449100 0.0082895 0.0222445 -0.0372518 -4.4516300 99.85

3.025 -3.3955600 0.0105454 0.0235193 -0.0350296 -3.3965200 99.97

3.125 -2.5780700 0.0118609 0.0234633 -0.0330136 -2.5757600 100.09

3.225 -1.9454700 0.0124985 0.0226469 -0.0311780 -1.9415000 100.20

3.325 -1.4600600 0.0126354 0.0214541 -0.0295010 -1.4554700 100.32

5

2.825 -8.6371600 -0.0238427 0.0770242 -0.0486771 -8.6326500 100.05

2.925 -6.6935800 -0.0185794 0.0771373 -0.0459368 -6.6809600 100.19

3.025 -5.1581700 -0.0145455 0.0753837 -0.0434429 -5.1407700 100.34

3.125 -3.9584100 -0.0114704 0.0725040 -0.0411647 -3.9385400 100.50

3.225 -3.0268100 -0.0091289 0.0690134 -0.0390758 -3.0060000 100.69

3.325 -2.2919700 -0.0073697 0.0652748 -0.0371536 -2.2712100 100.91

6

2.825 -8.6341500 -0.0259481 0.0489777 -0.0426850 -8.6538100 99.77

2.925 -6.7649200 -0.0185392 0.0515617 -0.0402109 -6.7721100 99.89

3.025 -5.2718700 -0.0130305 0.0511891 -0.0379651 -5.2716700 100.00

3.125 -4.0920500 -0.0089577 0.0490449 -0.0359182 -4.0878800 100.10

3.225 -3.1649200 -0.0059782 0.0459344 -0.0340456 -3.1590100 100.19

3.325 -2.4350000 -0.0038355 0.0423882 -0.0323268 -2.4287700 100.26


107

7

2.825 -6.3439100 -0.0008079 0.1601130 -0.0446853 -6.2292900 101.84

2.925 -4.8702400 -0.0007546 0.1404440 -0.0421074 -4.7726600 102.04

3.025 -3.7187100 -0.0005144 0.1236560 -0.0397662 -3.6353400 102.29

3.125 -2.8191100 -0.0002304 0.1093600 -0.0376309 -2.7476100 102.60

3.225 -2.1278400 0.0000373 0.0972072 -0.0356767 -2.0662700 102.98

3.325 -1.5945700 0.0002389 0.0868906 -0.0338823 -1.5413200 103.45

8

2.825 -0.0065126 0.0424602 -0.0140986 -0.0606358 -0.0387867 16.79

2.925 0.0932412 0.0374877 -0.0125142 -0.0554818 0.0627329 148.63

3.025 0.1433280 0.0331336 -0.0112246 -0.0509129 0.1143240 125.37

3.125 0.1589070 0.0293612 -0.0100983 -0.0468571 0.1313130 121.01

3.225 0.1547720 0.0261089 -0.0090655 -0.0432445 0.1285710 120.38

3.325 0.1401710 0.0233153 -0.0081110 -0.0400161 0.1153590 121.51

9

2.825 -3.8412100 0.0218847 -0.0399006 -0.0573358 -3.9165600 98.08

2.925 -2.9196000 0.0231508 -0.0299731 -0.0532334 -2.9796600 97.98

3.025 -2.2028100 0.0233431 -0.0226304 -0.0495549 -2.2516500 97.83

3.125 -1.6537800 0.0228383 -0.0171975 -0.0462446 -1.6943800 97.60

3.225 -1.2342900 0.0218951 -0.0131471 -0.0432560 -1.2688000 97.28

3.325 -0.9143350 0.0206784 -0.0101024 -0.0405491 -0.9443080 96.83

10

2.825 -5.0430248 0.0112429 0.0012606 -0.0312384 -5.0617512 99.63

2.925 -3.9877650 0.0108981 0.0040728 -0.0293312 -4.0021290 99.64

3.025 -3.1304585 0.0104404 0.0056437 -0.0276050 -3.1419749 99.63

3.125 -2.4431769 0.0099019 0.0063992 -0.0260362 -2.4529119 99.60

3.225 -1.8972484 0.0093185 0.0066469 -0.0246053 -1.9058893 99.55

3.325 -1.4671574 0.0087180 0.0066010 -0.0232960 -1.4751389 99.46

11

2.825 -5.7626112 0.0081290 -0.0051309 -0.0318689 -5.7914934 99.50

2.925 -4.5365971 0.0078691 -0.0016199 -0.0300013 -4.5603594 99.48

3.025 -3.5495101 0.0075152 0.0005860 -0.0283064 -3.5697094 99.43

3.125 -2.7569817 0.0071012 0.0019020 -0.0267618 -2.7747402 99.36

3.225 -2.1339030 0.0066569 0.0026323 -0.0253497 -2.1499643 99.25

3.325 -1.6435928 0.0062063 0.0029931 -0.0240543 -1.6584477 99.10

12

2.825 -9.4753289 -0.0079882 -0.0035862 -0.0332475 -9.5201602 99.53

2.925 -7.5293777 -0.0088041 -0.0003627 -0.0314226 -7.5699727 99.46

3.025 -5.9442648 -0.0091312 0.0018270 -0.0297575 -5.9813249 99.38

3.125 -4.6686922 -0.0091330 0.0032552 -0.0282329 -4.7028066 99.27

3.225 -3.6511519 -0.0089259 0.0041419 -0.0268324 -3.6827554 99.14

3.325 -2.8424500 -0.0085870 0.0046485 -0.0255417 -2.8719354 98.97

13

2.825 -7.8771000 -0.0100444 0.1495560 -0.0475216 -7.7851100 101.18

2.925 -6.0514700 -0.0098800 0.1336920 -0.0447581 -5.9724100 101.32

3.025 -4.6218300 -0.0093202 0.1201630 -0.0422482 -4.5532400 101.51

3.125 -3.5144200 -0.0085856 0.1085420 -0.0399601 -3.4544200 101.74

3.225 -2.6609300 -0.0077988 0.0985066 -0.0378669 -2.6080900 102.03

3.325 -2.0001200 -0.0070462 0.0898050 -0.0359449 -1.9533100 102.40


108

14

2.825 -8.0504779 -0.0086993 0.0019223 -0.0351461 -8.0923915 99.48

2.925 -6.3727006 -0.0097991 0.0023905 -0.0331664 -6.4132675 99.37

3.025 -5.0120525 -0.0101808 0.0027250 -0.0313618 -5.0508660 99.23

3.125 -3.9226503 -0.0101107 0.0029358 -0.0297108 -3.9595421 99.07

3.225 -3.0599713 -0.0097701 0.0030532 -0.0281957 -3.0948853 98.87

3.325 -2.3747518 -0.0092785 0.0031025 -0.0268011 -2.4077299 98.63

15

2.825 -8.8160037 -0.0147454 -0.0083638 0.0112335 -8.8488136 99.63

2.925 -7.0870689 -0.0087491 0.0120321 -0.0337284 -7.1175081 99.57

3.025 -5.6569857 -0.0087716 0.0122744 -0.0319444 -5.6854330 99.50

3.125 -4.4917659 -0.0085585 0.0121476 -0.0303102 -4.5184879 99.41

3.225 -3.5477006 -0.0082177 0.0117955 -0.0288083 -3.5729357 99.29

3.325 -2.7903526 -0.0077974 0.0113178 -0.0274235 -2.8142551 99.15

16

2.825 -8.2436899 -0.0097808 0.0081368 -0.0337594 -8.2790948 99.57

2.925 -6.5982315 -0.0101530 0.0088711 -0.0318835 -6.6314061 99.50

3.025 -5.2452002 -0.0101079 0.0091352 -0.0301724 -5.2763408 99.41

3.125 -4.1488545 -0.0098008 0.0090849 -0.0286063 -4.1781856 99.30

3.225 -3.2638301 -0.0093544 0.0088430 -0.0271679 -3.2915059 99.16

3.325 -2.5570505 -0.0088253 0.0084941 -0.0258431 -2.5832255 98.99


109

Table 8. Raw data obtained from calculations (CAM-B3LYP/6-311++G(d,p)) of


Model

Structure



1

2.825 -6.2104200 0.0006354 0.2383710 -0.0378105 -6.0092200 103.35

2.925 -4.8158300 -0.0011225 0.2062680 -0.0356041 -4.6462900 103.65

3.025 -3.6902000 -0.0021042 0.1791590 -0.0336026 -3.5467500 104.04

3.125 -2.8359600 -0.0025646 0.1562930 -0.0317799 -2.7140200 104.49

3.225 -2.1588400 -0.0027119 0.1370110 -0.0301135 -2.0546500 105.07

3.325 -1.6102800 -0.0027199 0.1207470 -0.0285847 -1.5208400 105.88

2

2.825 -6.4276600 -0.0056128 0.2037530 -0.0446052 -6.2741200 102.45

2.925 -4.9976400 -0.0049976 0.1777020 -0.0421144 -4.8670500 102.68

3.025 -3.8414700 -0.0043257 0.1551460 -0.0398466 -3.7305000 102.97

3.125 -2.9557000 -0.0036523 0.1357460 -0.0377741 -2.8613800 103.30

3.225 -2.2586300 -0.0030270 0.1191450 -0.0358729 -2.1783800 103.68

3.325 -1.6914400 -0.0025173 0.1049920 -0.0341229 -1.6230900 104.21

3

2.825 -9.0551400 -0.0256854 0.1088650 -0.0419433 -9.0139000 100.46

2.925 -7.1200400 -0.0207014 0.1042500 -0.0394793 -7.0759700 100.62

3.025 -5.5681900 -0.0167037 0.0988112 -0.0372440 -5.5233300 100.81

3.125 -4.3144800 -0.0135585 0.0930015 -0.0352083 -4.2702400 101.04

3.225 -3.3335000 -0.0110549 0.0871303 -0.0333473 -3.2907700 101.30

3.325 -2.5535900 -0.0090947 0.0814030 -0.0316400 -2.5129200 101.62

4

2.825 -7.1509900 -0.0019952 0.1554770 -0.0408194 -7.0383300 101.60

2.925 -5.5707300 -0.0014109 0.1368530 -0.0384047 -5.4736900 101.77

3.025 -4.3104500 -0.0007735 0.1207300 -0.0362150 -4.2267100 101.98

3.125 -3.3226400 -0.0001830 0.1068230 -0.0342220 -3.2502300 102.23

3.225 -2.5426600 0.0003509 0.0948642 -0.0324011 -2.4798500 102.53

3.325 -1.9248700 0.0007476 0.0846023 -0.0307318 -1.8702500 102.92

5

2.825 -11.3519000 -0.0000491 0.0587627 -0.0469496 -11.3402000 100.10

2.925 -8.9184400 -0.0000178 0.0642715 -0.0443818 -8.8985700 100.22

3.025 -6.9600600 -0.0001478 0.0664115 -0.0420362 -6.9358300 100.35

3.125 -5.4113300 -0.0003671 0.0663145 -0.0398857 -5.3852700 100.48

3.225 -4.1959700 -0.0005823 0.0647892 -0.0379071 -4.1696700 100.63

3.325 -3.2160800 -0.0008257 0.0624041 -0.0360810 -3.1905800 100.80

6

2.825 -11.0661000 -0.0140711 0.0547235 -0.1367140 -11.0675000 99.99

2.925 -8.7333600 -0.0095469 0.0582667 -0.0397536 -8.7243900 100.10

3.025 -6.8520700 -0.0061800 0.0584133 -0.0376087 -6.8374400 100.21

3.125 -5.3524900 -0.0037196 0.0564311 -0.0356474 -5.3354200 100.32

3.225 -4.1732400 -0.0019123 0.0532124 -0.0338471 -4.1557800 100.42

3.325 -3.2355700 -0.0006361 0.0493699 -0.0321893 -3.2190200 100.51


110

7

2.825 -7.1771300 -0.0009220 0.2193690 -0.0448664 -7.0035500 102.48

2.925 -5.5848300 -0.0025383 0.1904710 -0.0423171 -5.4392200 102.68

3.025 -4.2988900 -0.0033561 0.1662810 -0.0399979 -4.1759700 102.94

3.125 -3.3196100 -0.0036502 0.1459850 -0.0378803 -3.2151500 103.25

3.225 -2.5300200 -0.0036433 0.1289110 -0.0359396 -2.4407000 103.66

3.325 -1.8971400 -0.0035336 0.1145110 -0.0341552 -1.8203200 104.22

8

2.825 -0.1206650 0.0298742 0.0218952 -0.0610709 -0.1299660 92.84

2.925 0.0040753 0.0264024 0.0202067 0.0525804 0.0049529 82.28

3.025 0.0732845 0.0233542 0.0186079 -0.0514273 0.0638193 114.83

3.125 0.1084270 0.0207182 0.0171776 -0.0474058 0.0989171 109.61

3.225 0.1225330 0.0184569 0.0159364 -0.0438214 0.1131050 108.34

3.325 0.1202560 0.0165275 0.0148781 -0.0406157 0.1110460 108.29

9

2.825 -4.5047000 0.0174908 -0.0294744 -0.0576875 -4.5743700 98.48

2.925 -3.4852900 0.0192342 -0.0194277 -0.0536179 -3.5391100 98.48

3.025 -2.6966300 0.0198243 -0.0122374 -0.0499668 -2.7390100 98.45

3.125 -2.0582200 0.0196516 -0.0071149 -0.0466796 -2.0923600 98.37

3.225 -1.5614900 0.0190038 -0.0034815 -0.0437098 -1.5896700 98.23

3.325 -1.1932200 0.0180825 -0.0009137 -0.0410180 -1.2170700 98.04

10

2.825 -6.40650637 0.003593 0.0012969 -0.0324108 -6.43402794 99.57

2.925 -5.15837125 0.0031398 0.0041538 -0.0305393 -5.18161448 99.55

3.025 -4.12193613 0.0028182 0.0057513 -0.0288368 -4.14219155 99.51

3.125 -3.27551482 0.0025756 0.0065112 -0.0272824 -3.29370823 99.45

3.225 -2.5834359 0.0023894 0.0067366 -0.0258583 -2.60017046 99.36

3.325 -2.02571045 0.002235 0.006641 -0.0245496 -2.04137894 99.23

11

2.825 -7.03722989 0.0016791 -0.0087616 -0.0323207 -7.07663258 99.44

2.925 -5.62066897 0.0012662 -0.0039705 -0.0305045 -5.65387159 99.41

3.025 -4.46000809 0.0009776 -0.0008647 -0.0288497 -4.48875003 99.36

3.125 -3.51733145 0.0007717 0.001067 -0.0273364 -3.54283308 99.28

3.225 -2.76022196 0.0006309 0.0021991 -0.0259478 -2.78333895 99.17

3.325 -2.1518299 0.0005283 0.0028024 -0.02467 -2.17316543 99.02

12

2.825 -10.8649434 -0.0052768 -0.0150692 -0.0339372 -10.919215 99.50

2.925 -8.81169737 -0.0057432 -0.0091936 -0.0320781 -8.85871688 99.47

3.025 -7.10437858 -0.0059399 -0.0050001 -0.0303803 -7.145703 99.42

3.125 -5.68628868 -0.0059786 -0.0020591 -0.0288248 -5.72315243 99.36

3.225 -4.53797182 -0.0058756 -3.86E-05 -0.0273948 -4.57128666 99.27

3.325 -3.60076583 -0.0056974 0.0013184 -0.0260759 -3.6312191 99.16

13

2.825 -8.7675500 -0.0129312 0.1443740 -0.0475191 -8.6836200 100.97

2.925 -6.8426300 -0.0119873 0.1298540 -0.0447587 -6.7695300 101.08

3.025 -5.3049300 -0.0108222 0.1173480 -0.0422508 -5.2406600 101.23

3.125 -4.1119300 -0.0095903 0.1064880 -0.0399636 -4.0550000 101.40

3.225 -3.1414500 -0.0084381 0.0970003 -0.0378700 -3.0907600 101.64

3.325 -2.3753500 -0.0074290 0.0886742 -0.0359474 -2.3300500 101.94


111

14

2.825 -9.0404265 -0.0068039 -0.0018878 -0.0350812 -9.0842057 99.52

2.925 -7.3035242 -0.0078135 -0.0004817 -0.0331109 -7.3449327 99.44

3.025 -5.8600168 -0.0082183 0.0005164 -0.0313136 -5.8990407 99.34

3.125 -4.6634180 -0.0082495 0.0011968 -0.0296683 -4.7001414 99.22

3.225 -3.7051991 -0.0080141 0.0016384 -0.0281574 -3.7397343 99.08

3.325 -2.9226160 -0.0076477 0.0019098 -0.0267659 -2.9551173 98.90

15

2.825 -10.0110455 -0.0074487 0.0056522 -0.0354680 -10.0483161 99.63

2.925 -8.2127036 -0.0075159 0.0079111 -0.0335297 -8.2458361 99.60

3.025 -6.6946271 -0.0073663 0.0092236 -0.0317595 -6.7245193 99.56

3.125 -5.4119427 -0.0071100 0.0098740 -0.0301371 -5.4393100 99.50

3.225 -4.3603441 -0.0067643 0.0100748 -0.0286451 -4.3856774 99.42

3.325 -3.4965009 -0.0063814 0.0099850 -0.0272689 -3.5201650 99.33

16

2.825 -9.3518606 -0.0082658 0.0034613 -0.0335584 -9.3902253 99.59

2.925 -7.6401092 -0.0084667 0.0053658 -0.0316985 -7.6749109 99.55

3.025 -6.2019463 -0.0083684 0.0064717 -0.0300009 -6.2338443 99.49

3.125 -4.9872101 -0.0081144 0.0070226 -0.0284462 -5.0167376 99.41

3.225 -4.0040086 -0.0077290 0.0072001 -0.0270176 -4.0315442 99.32

3.325 -3.1970882 -0.0072891 0.0071397 -0.0257008 -3.2229405 99.20


(BHandHLYP/6-311++G(d,p)).

𝑦 = 𝐀𝑥2 + 𝐁𝑥 + 𝐂

iso

/ ppm

Model A B C R2

1 -9.88 69.06 -121.84 0.9995

2 -10.17 71.13 -125.62 0.9996

3 -13.52 95.20 -169.38 0.9998

4 -11.34 79.53 -140.83 0.9996

5 -16.19 113.58 -201.50 0.9998

6 -15.94 112.14 -199.48 0.9998

7 -11.13 77.97 -137.96 0.9997

8 -1.46 9.41 -15.08 0.9941

9 -7.41 51.85 -91.61 0.9998

10 -8.32 59.50 -107.81 0.9999

11 -10.57 75.06 -134.91 0.9999

12 -13.31 95.41 -173.40 0.9999

13 -13.31 93.66 -166.45 0.9996

14 -11.45 81.99 -148.84 0.9999

15 -11.27 81.61 -150.02 1.0000


112

16 -10.94 78.93 -144.54 1.0000


(LC-PBE-D3/6-311++G(d,p)).

𝑦 = 𝐀𝑥2 + 𝐁𝑥 + 𝐂

iso

/ ppm

Model A B C R2

1 -10.65 73.88 -129.32 0.9997

2 -11.00 76.40 -133.87 0.9997

3 -14.34 99.96 -175.87 0.9997

4 -10.71 74.46 -130.65 0.9997

5 -15.21 106.10 -186.97 0.9997

6 -14.36 100.66 -178.37 0.9998

7 -11.58 80.46 -141.12 0.9997

8 -1.41 8.97 -14.09 0.9849

9 -7.63 52.78 -92.14 0.9996

10 -7.85 55.40 -98.91 0.9998

11 -9.22 64.88 -115.51 0.9998

12 -14.23 100.74 -180.47 0.9999

13 -14.43 100.28 -175.87 0.9997

14 -12.41 87.61 -156.52 0.9998

15 -12.16 86.77 -156.92 0.9999

16 -11.73 83.47 -150.43 0.9999


113


(CAM-B3LYP/6-311++G(d,p)).

𝑦 = 𝐀𝑥2 + 𝐁𝑥 + 𝐂

iso

/ ppm

Model A B C R2

1 -10.55 73.73 -130.11 0.9996

2 -10.84 75.89 -134.10 0.9997

3 -14.45 101.77 -181.15 0.9998

4 -11.93 83.61 -147.98 0.9997

5 -18.40 129.27 -229.68 0.9998

6 -17.61 123.85 -220.38 0.9998

7 -11.92 83.55 -147.89 0.9996

8 -1.54 9.93 -15.87 0.9861

9 -8.04 56.10 -98.88 0.9998

10 -8.66 62.01 -112.46 0.9999

11 -10.15 72.17 -129.93 0.9999

12 -14.01 100.67 -183.46 0.9999

13 -14.33 100.70 -178.77 0.9997

14 -11.99 85.94 -156.14 0.9999

15 -11.71 85.00 -156.72 1.0000

16 -11.35 82.10 -150.70 1.0000


114


chemical shift vs the carbon tetrel bond length (MP2/6-311++G(d,p)).

𝑦 = 𝐀𝑥2 + 𝐁𝑥 + 𝐂

Energy

/ kcal/mol iso

/ ppm

Model A B C R2 A B C R2

1 6.45 -42.81 71.12 0.9977 8.03 -57.07 98.07 0.9999

2 6.45 -42.71 70.68 0.9976 7.94 -56.63 97.63 0.9999

3 3.18 -17.27 14.43 0.9981 2.79 -20.61 59.49 1.0000

4 5.61 -36.78 59.84 0.9970 6.06 -43.39 96.62 0.9999

5 2.77 -13.61 4.74 0.9988 2.53 -19.03 57.35 1.0000

6 5.86 -37.00 54.96 0.9841 4.36 -32.79 81.43 1.0000

7 5.61 -36.84 60.07 0.9968 6.67 -47.72 114.32 0.9999

8 16.96 -112.74 185.57 0.9985 0.18 -1.65 117.48 1.0000

9 5.11 -31.55 45.58 0.9602 0.46 -4.03 106.67 0.9999

10 8.21 -54.40 89.68 0.9977 7.29 -53.12 124.51 1.0000

11 7.86 -51.93 85.01 0.9977 6.97 -50.59 89.30 0.9999

12 8.52 -52.83 72.35 0.9802 2.31 -17.77 37.11 1.0000

13 4.02 -25.56 39.04 0.9896 2.93 -21.54 99.57 1.0000

14 6.34 -41.03 64.63 0.9950 1.63 -13.33 86.88 1.0000

15 5.93 -34.94 40.13 0.9905 2.55 -19.99 67.94 1.0000

16 6.11 -36.99 47.08 0.9722 2.85 -21.77 70.35 1.0000


115


chemical shift vs the carbon tetrel bond length (B3LYP/6-311++G(d,p)).

𝑦 = 𝐀𝑥2 + 𝐁𝑥 + 𝐂

Energy

/ kcal/mol iso

/ ppm


1 6.11 -40.88 68.95 0.9981 8.99 -63.78 124.20 0.9998

2 6.18 -41.38 69.78 0.9978 8.66 -61.83 121.34 0.9999

3 2.77 -14.73 10.60 0.9984 2.63 -19.68 73.61 1.0000

4 5.20 -34.42 57.00 0.9972 7.22 -51.48 125.71 0.9998

5 3.79 -20.13 14.64 0.9984 2.02 -15.67 67.25 1.0000

6 7.29 -46.46 70.62 0.9900 4.26 -32.20 95.89 1.0000

7 5.20 -34.42 57.04 0.9972 7.44 -53.15 137.63 0.9999

8 16.29 -108.65 180.38 0.9986 0.23 -2.08 140.37 0.9999

9 5.52 -35.22 54.19 0.9901 0.34 -2.88 122.95 1.0000

10 7.95 -53.04 88.76 0.9982 7.88 -57.50 147.77 0.9999

11 7.59 -50.54 83.87 0.9979 7.03 -51.35 109.29 0.9999

12 4.84 -28.47 32.59 0.9909 0.72 -6.79 40.43 0.9999

13 3.61 -23.10 35.70 0.9895 3.18 -23.33 119.54 1.0000

14 5.86 -38.12 60.76 0.9954 1.25 -10.87 99.52 0.9999

15 5.45 -31.99 35.80 0.9896 2.06 -16.62 77.16 1.0000

16 5.77 -35.04 44.74 0.9738 2.40 -18.73 80.11 1.0000


116


chemical shift vs the carbon tetrel bond length (LC-PBE/6-311++G(d,p)).

𝑦 = 𝐀𝑥2 + 𝐁𝑥 + 𝐂

Energy

/ kcal/mol iso

/ ppm


1 6.11 -40.86 68.72 0.9985 8.35 -59.03 103.83 0.9998

2 6.11 -40.86 68.71 0.9985 8.18 -58.14 102.65 0.9998

3 2.93 -15.78 12.06 0.9986 2.99 -21.97 64.67 1.0000

4 5.11 -34.02 56.50 0.9981 5.34 -38.06 88.83 0.9999

5 2.61 -12.63 2.85 0.9991 2.61 -19.65 61.18 1.0000

6 5.36 -33.87 50.46 0.9832 4.61 -34.36 85.92 1.0000

7 5.25 -34.78 57.54 0.9975 6.40 -45.61 111.28 0.9998

8 17.46 -116.06 191.31 0.9984 -0.04 -0.20 122.68 0.9997

9 6.32 -40.05 60.84 0.9881 0.17 -1.78 110.17 0.9998

10 7.70 -51.40 85.88 0.9982 7.42 -53.56 126.94 0.9999

11 7.43 -49.41 81.74 0.9979 7.06 -50.88 92.70 0.9999

12 5.18 -30.74 36.23 0.9893 1.92 -14.94 38.19 1.0000

13 3.75 -24.00 36.97 0.9922 2.96 -21.75 106.24 1.0000

14 5.84 -38.02 60.45 0.9962 1.54 -12.63 91.72 1.0000

15 5.52 -32.49 36.55 0.9903 2.86 -21.94 73.64 1.0000

16 5.77 -35.01 44.38 0.9709 3.09 -23.29 75.34 1.0000


117


chemical shift vs the carbon tetrel bond length (LC-PBE-D3/6-311++G(d,p)).

𝑦 = 𝐀𝑥2 + 𝐁𝑥 + 𝐂

Energy

/ kcal/mol iso

/ ppm


1 5.61 -36.78 60.15 0.9957 8.35 -59.03 103.83 0.9998

2 5.70 -37.19 60.41 0.9950 8.18 -58.14 102.65 0.9998

3 2.45 -11.88 3.89 0.9988 2.99 -21.97 64.67 1.0000

4 4.86 -31.39 49.96 0.9912 5.34 -38.06 88.83 0.9999

5 2.27 -9.48 -4.51 0.9994 2.61 -19.65 61.18 1.0000

6 5.20 -31.90 45.11 0.9422 4.61 -34.36 85.92 1.0000

7 4.79 -30.90 49.19 0.9921 6.40 -45.61 111.28 0.9998

8 18.61 -121.47 195.17 0.9970 -0.04 -0.20 122.68 0.9997

9 5.61 -33.99 47.51 0.9622 0.17 -1.78 110.17 0.9998

10 8.20 -53.65 87.14 0.9961 7.42 -53.56 126.94 0.9999

11 8.04 -52.37 84.22 0.9959 7.06 -50.88 92.70 0.9999

12 5.61 -32.69 37.37 0.9908 1.92 -14.94 38.19 1.0000

13 3.52 -21.69 31.35 0.9596 2.96 -21.75 106.24 1.0000

14 6.34 -40.46 62.49 0.9863 1.54 -12.63 91.72 1.0000

15 6.11 -35.36 38.95 0.9936 2.86 -21.94 73.64 1.0000

16 6.29 -37.49 46.29 0.9855 3.09 -23.29 75.34 1.0000


118


chemical shift vs the carbon tetrel bond length (CAM-B3LYP/6-311++G(d,p)).

𝑦 = 𝐀𝑥2 + 𝐁𝑥 + 𝐂

Energy

/ kcal/mol iso

/ ppm


1 5.61 -36.98 61.14 0.9963 -10.69 55.96 -63.08 0.9561

2 5.70 -37.54 62.01 0.9971 -11.62 61.38 -70.98 0.9553

3 2.27 -10.82 2.68 0.9989 -12.06 68.58 -63.97 0.9237

4 4.77 -31.00 50.02 0.9948 -11.68 63.51 -54.65 0.9465

5 3.95 -20.46 13.45 0.9986 -13.47 77.25 -77.11 0.9170

6 6.45 -40.19 58.71 0.9685 -24.41 139.96 -167.83 0.9151

7 4.93 -32.05 51.83 0.9956 -13.10 71.44 -56.33 0.9454

8 16.36 -107.80 175.74 0.9979 -5.32 31.28 83.70 0.8709

9 5.20 -31.95 46.05 0.9459 -6.02 35.24 61.38 0.8863

10 7.61 -50.21 82.69 0.9975 -15.52 84.24 -71.99 0.9510

11 7.36 -48.43 79.00 0.9967 -13.17 70.81 -81.88 0.9544

12 4.93 -28.51 31.26 0.9932 -11.08 63.10 -70.63 0.9291

13 3.27 -20.17 29.37 0.9569 -12.73 72.49 -28.91 0.9203

14 5.54 -35.39 54.82 0.9911 -13.21 75.66 -33.95 0.9243

15 5.27 -30.21 31.43 0.9950 -16.97 97.22 -97.67 0.9213

16 5.45 -32.33 38.81 0.9861 -14.34 81.48 -74.55 0.9285


119


chemical shift vs the carbon tetrel bond length (BHandHLYP/6-311++G(d,p)).

𝑦 = 𝐀𝑥2 + 𝐁𝑥 + 𝐂

Energy

/ kcal/mol iso

/ ppm


1 5.77 -38.18 63.44 0.9973 8.46 -59.99 110.80 0.9998

2 5.95 -39.28 65.11 0.9972 8.24 -58.78 109.17 0.9999

3 2.43 -11.88 4.28 0.9990 2.93 -21.59 68.61 1.0000

4 4.91 -32.04 51.97 0.9952 6.70 -47.77 111.05 0.9999

5 3.12 -15.25 5.37 0.9988 2.48 -18.72 64.19 1.0000

6 6.04 -37.67 55.17 0.9719 4.70 -34.98 91.78 1.0000

7 4.84 -31.59 51.33 0.9946 6.96 -49.71 123.23 0.9999

8 16.61 -109.81 179.85 0.9981 0.20 -1.78 122.32 1.0000

9 5.20 -32.14 46.79 0.9630 0.36 -3.05 108.91 1.0000

10 7.70 -50.95 84.26 0.9972 7.77 -56.44 137.17 0.9999

11 7.86 -51.80 84.74 0.9980 7.73 -56.24 109.68 0.9999

12 5.02 -29.15 32.41 0.9934 2.01 -15.77 46.55 1.0000

13 3.34 -20.74 30.48 0.9662 3.19 -23.33 109.11 1.0000

14 5.68 -36.45 56.82 0.9919 1.92 -15.42 96.84 1.0000

15 5.34 -30.75 32.47 0.9943 2.86 -22.10 78.15 1.0000

16 5.61 -33.41 40.63 0.9877 3.11 -23.56 80.00 1.0000


120

Table 18. CP-corrected energy and the 13C isotropic chemical shift vs the carbon tetrel

bond angle (CAM-B3LYP/6-311++G(d,p)). In all cases the angle was set so that the

oxygen or nitrogen was placed between two methyl hydrogen atoms.

Interaction energy

/ kcal/mol iso

/ ppm

Model Structure Model Structure

Angle

/ degrees 12 13 16 12 13 16

140 -9.19 -0.73 -8.17 21.34 75.33 43.44

145 -9.34 -0.91 -8.33 20.88 75.14 43.07

150 -9.49 -1.08 -8.51 20.46 74.95 42.68

155 -9.64 -1.25 -8.69 20.09 74.78 42.31

160 -9.77 -1.40 -8.86 19.79 74.64 41.98

165 -9.88 -1.53 -9.01 19.56 74.54 41.72

170 -9.95 -1.63 -9.12 19.42 74.48 41.53

175 -10.00 -1.69 -9.19 19.36 74.48 41.42

180 -10.00 -1.71 -9.21 19.38 74.51 41.40

Appendix II – Sample of Computation Input Files

121


Gaussian Input for the Geometry Optimization of Acetylene

%nprocshared=4

%mem=200MW

%chk=acetylene.chk

# opt freq B3LYP/6-311++g(d,p)

Acetylene

0 1

O -2.38476950 0.11022044 0.00000000

C -3.64316950 0.11022044 0.00000000

C -4.15650238 0.79185828 1.28197473

H -3.79983653 1.80004974 1.31718059

H -5.22650238 0.79185682 1.28197551

H -3.79983440 0.25727357 2.13749044

C -4.15650310 -1.34082091 -0.05067148

H -5.22650116 -1.34089227 -0.04863256

H -3.80150292 -1.81380188 -0.94239110

H -3.79817192 -1.87595925 0.80380246

1 2 2.0

2 3 1.0 7 1.0

3 4 1.0 5 1.0 6 1.0

4

5


122

Gaussian Input for NMR calculation of Magnetic Shielding Contributions

%nprocshared=4

%mem=200MB

%chk=1.chk

# nmr lc-wpbe/6-311++g(d,p) empiricaldispersion=GD3

counterpoise=2 iop33(10=1)

Mag Sheild

0 1 0 1 0 1

C(Fragment=1) -0.02693000 -0.00289400 0.88347900

H(Fragment=1) -0.02717500 1.01401200 1.28351400

H(Fragment=1) 0.85369700 -0.51146400 1.28346400

H(Fragment=1) -0.90768000 -0.51156100 1.28308900

C(Fragment=1) -0.02685700 -0.00297000 -0.63762200

H(Fragment=1) 0.85055600 0.50421000 -1.04042300

H(Fragment=1) -0.02566900 -1.01586600 -1.04086500

H(Fragment=1) -0.90319800 0.50525200 -1.04080600

C(Fragment=2) -0.02729300 -0.00348000 -4.66034000

H(Fragment=2) -0.35968700 0.87559200 -5.24404400

H(Fragment=2) 0.30474000 -0.88301700 -5.24355300

O(Fragment=2) -0.02685700 -0.00297000 -3.46262200


123

Gaussian Input for NMR calculation of J-coupling

%nprocshared=4

%mem=200MB

%chk=2.chk

# nmr=spinspin cam-b3lyp/6-311++g(d,p) Counterpoise=2

J-coupling

1 1 1 1 0 1

C(Fragment=1) 3.54568454 0.01569282 0.23519796

H(Fragment=1) 3.91235854 0.89998582 -0.27818404

H(Fragment=1) 3.81597554 0.02344182 1.28480996

H(Fragment=1) 3.91092554 -0.87688118 -0.26470304

S(Fragment=1) 1.71996354 0.01562582 0.03088496

H(Fragment=1) 1.37618554 -0.97148218 0.88942096

H(Fragment=1) 1.37770954 1.01555082 0.87508296

N(Fragment=2) 6.46194146 0.01570318 0.46118604

C(Fragment=2) 7.60343946 0.01541618 0.51346204

H(Fragment=2) 8.67209546 0.01514518 0.56245804

1 2 1.0 3 1.0 4 1.0 5 1.0

2

3

4

5 6 1.0 7 1.0

6

7

8 9 3.0

9 10 1.0

10

Documents

Investigations of Non-Covalent Carbon Tetrel Bonds by Computational Chemistry … · 2017-01-31 · Investigations of Non-Covalent Carbon Tetrel Bonds by Computational Chemistry and